Basic Electrical Engineering
Question Bank
Unit 1
UNIT 1 – ELEMENTORY CONCEPTS
1. Define electrical resistivity. State the factors on which it depends.
2. Derive the relationships for the equivalent resistance of a combination of two resistances
R1 and R2 in parallel as well as the shares I1 and I2 of total current I when connected to
supply mains (In terms of I, R1 and R2) from the first principles.
3. Define resistance temperature coefficient (RTC). State its unit and if it is true that RTC
can have (i) zero value (ii) positive value (iii) negative value, then prove it.
4. Derive the relationship with usual notations, (i) α2= α1/ [1+ α1 (t2 –t1)] and hence obtain,
αt= α0/ [1+ α0t] and α0= αt / [1- αt t].
5. Derive the expression α2= 1/ [(1/ α1 )+ (t2 –t1)]. The symbols have their usual meaning.
6. For a metallic conductor, define the temperature coefficient of resistance. How is its
value affected by temperature? Derive an expression for RTC in terms of α1 at
temperature t1 0C in terms of α0 at temperature 00C.
7. With usual notations prove that, α1 –α2 =, α1 α2 (t2 – t1).
8. Define resistance temperature coefficient (RTC). α1 at temperature t1 0C and α2 at
temperature t20C, then prove that- α1 /α2 = 1+α1 (t2 – t1).
9. Define resistivity. Derive the expression ρ2 = ρ1 [1+ α1 (t2 – t1)].
10. Define Insulation resistance. Derive the expression for insulation resistance of the cable
having length ‘l’, resistivity of the conductor ‘ρ’ and R1 and R2 are radii of conductor
and sheath respectively.
11. Prove that Ri= ρ/ (2πl) log (R2 / R1) for a cable.
12. A coil has resistance of 18 Ω when its mean temperature is 200 C and 20 Ω when its mean
temperature is 500 C. find its mean temperature rise when its resistance is 21 Ω and the
ambient temperature is 150 C. (ANS-500C)
13. A potential difference of 250 volt is applied to a copper field coil at the temperature of 15
0
C and the current is 5 ampere. What will be the mean temperature of the coil when the
current has fallen to 3.91 amperes, the applied voltage is maintained constant.(RTC of
copper at 00 C=0.00426/0 C)
(ANS-84.630C)
14. It is required to maintain a loading of 5 kW in a heating unit. At an initial temperature of
150 C a voltage of 200 V is necessary for this purpose. When the unit is settled down to a
steady temperature, a voltage of 220 V is required to maintain same loading. Estimate the
final temperature of the heating element, if the RTC of heating element is 0.0006/0 C.
(ANS-368.150C)
15. A coil has resistance of 50 Ω at 150 C and 58 Ω at 550 C. find the RTC at 00 C and 150
C.(ANS-0.00426/0C,0.004/0C)
16. The resistance of the copper wire is 50 Ω at a temperature of 35 0 C. if the wire is heated
to a temperature of 800 C, find the resistance at that temperature. Assume the RTC of
copper at 00 C= 0.00427/0 C, also find the RTC at 350 C.(ANS-58.35 Ohm,0.00372/0C)
17. Two resistances A of 80 Ω and B of 120 Ω at 00 C are connected in series. A has RTC of
0.0038/0 C and B has RTC of 0.0018 /0 C. Find RTC of series combination at 00 C.(ANS0.0026/0C)
18. The DC resistance of the coil when measured at room temperature of 250 C was 10. And
it was 10.5 when coil became hot ant attained stable temperature. The value of RTC at 00
C= 0.00426/0 C. calculate the stable temperature.(ANS-37.9870C)
19. Find the current flowing at the instant of switching 100 Watt lamp on a 240 Volt DC
supply. Given that, lamps working temperature is 20000 C and room temperature is 150 C.
(RTC at 00 C= 0.005/0 C) (ANS-4.26 amp)
20. The insulation resistance per km of the single core cable having conductor diameter of
1.2 cm and an insulation thickness of 1.4 cm is 550M Ω. What would be the insulation
resistance if the thickness of the insulation were increased to 2 cm?(ANS669.85MOhm/km)
21. An electric iron is marked 250 Volt, 350 Watt. What current does it take and what will be
its hot resistance? What is the weekly cost of using it for 30 min daily at 35 paise per
unit?(ANS-1.4A,178.57Ohm,43Paise)
22. An electric furnace is used to melt the 1000kg of tin per hour. If the input to the furnace
is 50 kW, find the efficiency of the furnace? Assume melting point of the furnace is 2350
C. specific latent heat of fusion for tin is 56kJ/kg and specific heat of the tin is
235J/kg0K. initial temperature of the charge is 150 C.(ANS-59.83%)
23. Find the power in kW taken by a DC motor driving a pump to raise 14000 litres of water
per min to a height of 30 m. the motor efficiency of 90% and pump efficiency is 75%.
Assume 1 litre of water to have a mass of 1 kg.
(ANS-101.73Kw)
24. A car weighing 8 kN reaches the bottom of a 1 I 20 slope at a speed of 60 km/h at which
point it runs out of petrol. How far up the slope will the car ascend,if the frictional
resistance to the motion is 160 N per kN of its weight?(ANS-67.45m)
25. Calculate the resistance of the element used to heat 10 litres of water from 20 0 C to 100 0
C in 1 hour. Efficiency if the operation is 90% and the supply voltage is 200 Volt
DC.(38.69 ohm)
26. Calculate the time required to heat the 15 litres of water from 150 C to the boiling point.
The heater is operated at 230 volt supply and resistance of the heating element is 40 ohm.
The efficiency of the heater is 84 % and assume the specific heat of water if 4180
J/kg0K.(ANS-80Minutes)
27. The average overall efficiency of a car is 50 % , if the car consumes 4 kg of petrol per
hour of calorific value 46.89 MJ/kg, determine the power output of the car engine.(ANS26.05kW)
28. A single core copper cable has conductor diameter of 2 cm and insulation thickness of
1.8 cm. The resistivities of copper and insulation are 1.73×10-6 and 8×1012 respectively.
Determine the resistance of the conductor and insulation of the cable for 100 m length.
(ANS-5.507miliohm,1.311×104megaohm)
Unit 2
1. Define magnetic flux, magnetic flux density, magnetic field strength and state its units.
2. Explain the magnetic field due to straight conductor. Explain the cross and dot
convention.
3. Explain the concept of magneto motive force and state its unit.
4. Define (i) reluctance (ii) permeance (iii) Absolute permeability (iv) permeability of free
space (v) Relative permeability and also state its units.
5. What is magnetic circuit? Derive the relation between m.m.f, flux and reluctance from it.
6. Write a note on series magnetic circuit.
7. Explain parallel magnetic circuit.
8. Compare electric and magnetic circuits clearly stating similarities and dissimilarities
between them.
9. Write a note on magnetic leakage and fringing.
10. What is dynamically induced e.m.f. ? Derive the expression for its magnitude.
11. What is statically induced e.m.f? Explain the phenomenon of self induced e.m.f?
12. Define self inductance? Derive expression for the self induced e.m.f and state its unit.
13. State the various factors affecting the self inductance of the coil.
14. Explain the phenomenon of mutually induced e.m.f
15. Define mutual inductance and state its units. Derive the expression for mutual inductance.
16. Define coefficient of coupling and obtain the relation between self inductances , mutual
inductance and coefficient of coupling.
17. Derive the expression for the energy stored in a magnetic field.
18. Obtain the expression for the energy stored per unit volume in an inductor.
19. An iron ring of circular cross sectional area of 3 cm2 and mean diameter of 20 cm is
wound with 500 turns of wire and carries a current of 2 Amp to produce the magnetic
field of 0.5 mWeb in the ring. Determine the permeability of the material.
( Ans: µr = 833.334)
20. An iron ring of 60 cm mean length has a circular cross section of 6 cm diameter. An air
gap of 2 mm is cut in it. A coil of 700 turns is uniformly wound around it and a current of
2 Amp passes through it. Calculate the flux produced in the air gap and in the ring, if the
relative permeability of iron is 1000. Ignore leakage and fringing. (Ans: ϕ = 1.91 mWb)
21. A rectangular core of iron has a uniformly wound coil of 260 turns on one limb and has
an air gap of 2.5 mm in the other limb. The mean length of the core is 320 mm and the
area of cross section is 4 sq cm. If the coil carries a current of 3.2 Amp, find the flux in
the air gap neglecting the magnetic the magnetic leakage and fringing. Assume relative
permeability of iron as 480. (ans: ϕ = 0.1323mWb)
22. A magnetic circuit has the mean length of flux path of 20 cm cross sectional area of 1
cm2. Relative permeability of its material is 2400. Find the mmf required to produce a
flux density of 2 Tesla in it. If an air gap of 1mm is introduced in it, Find the mmf
required for the air gap as a fraction of the total mmf to maintain the same flux density.
(Ans: MMF = 132.6291 A)
23. A coil is wound uniformly with 300 turns over a steel ring of relative permeability of
900 having mean circumference of 40 mm and area of cross section of 50 mm2. If a
current of 5 Amp is passed through the coil then find,(a) mmf (b) Flux (c) Reluctance of
the ring. (Ans: 1500A, 707355.3 A/Wb, 2.12 mWb)
24. An iron ring has its mean length of flux path as 60 cm and its cross sectional area as 15
cm2. Its relative permeability is 500. Find the current required to be passed through a coil
of 300 turns wound uniformly on it, tio produce a flux density of 1.2 tesla. What would
be the flux density with the same current, if the iron ring is replaced by an air core. (Ans:
I = 3.82 A, B = 2.4* 10-3 T )
25. A ring shaped core is made up of two parts of the same material. Part one is the magnetic
path of mean length 25 cm and with cross sectional area 4 cm2, whereas part two is of
length 10 cm and cross sectional area 6 cm2. The flux density in part 2 is 1.5 Tesla. If the
current through the coil wound over core is 0.5 A, calculate the number of turns of the
coil. Assume µr to be 1000 for the material.(Ans: N = 1134)
26. A ring has diameter of 21 cm and cross sectional area of 10 cm2. The ring is made up of
semi circular sections of cast iron and cast steel with each joint having a reluctance equal
to an air gap of 0.2 mm. find the ampere turns reuired to produce a flux of 0.0008 Web.
The relative permiabilities of cast steel and cast iron are 800 and 166 respectively.(Ans:
mmf = 1782.4)
27. Two coils A and B are placed such that 40% of flux produced by coil A is linking with
coil B. coils A and B have 2000 and 1000 turn respectively. A current of 2.5 Amp in coil
A produces a flux of 0.035 mWeb in coil B. for the abovr coil combination, find out (a)
M mutual inductance (b) the coefficient of couplings K,K1,K2 (c) self inductances L1,L2.
(Ans: 0.014 H, K = 0.4472, L1 = 0.07 H, L2 = 0.014 H)
28. Two coils with 1000 and 300 turns respectively are wound on a common magnetic
circuit. The two coils have perfect magnetic coupling between them. Reluctance of the
magnetic circuic is 3×106 Amp/Web. Find the mutual inductance between them. If the
current in 1000 turn changes uniformly from 5A to zero I 10 msec, find the emf induced
in the other coil.
29. Two long single layered solenoids X and Y have the same length and same no of turns.
The areas of their cross section are ax and ay respectively with ax < ay. they are placed
coaxially with solenoid Y placed within solenoid X. Show that the coefficient of coupling
between them is (ay/ax)1/2.
30. Consider a magnetic core in the form of closed ring of mean length of 20 cm and cross
sectional area of 1 sq cm. its relative permeability is 2400. A coil of 2000 turns is
uniformly wound around it. Find the flux density set up in the core of a current of 66 mA
is passed through the coil. Find the energy stored in the magnectic field set up. Find the
inductance of the coil if an air gap of 1 mm is cut in the ring perpendicular to the
direction of flux.
31. An iron ring wound with 500 turns solenoid produces a flux density of 0.94 Tesla in the
ring carring a current of 2.4Amp. the length of iron path is 80 cm and that of air gap is 1
mm determine, (relative permeability of iron) (b) self inductance (c) energy stored if the
area of cross section of the ring is 20 sq cm.
Unit 3
Questions on transformer
1. What is autotransformer? State its advantages. Disadvantages and applications?
2. Explain the working principal of transformer?
3. Compare core type and shell type construction of transformer?
4. Derive Emf equation of transformer.
( very imp question)
5. Why rating of transformer is specified in volt amperers and not in watts
6. Explain the magnetic leakage and its effect in transformer.
7. What is the regulation of transformer. Why secondary terminal voltage reduces on load?
8. Explain various losses in a transformer. In which part these losses occur?How to
minimize them?
9. Define efficiency of a transformer . how to obtain efficiency at various loads?
10. Derive the condition for the maximum efficiency for a transformer. ( IMP qustn)
11. With the help of neat circuit diagram , describe the method of testing a single phase
transformer by direct loading . Explain how efficiency and regulation are calculated from
test results. (VIMP)
Question on Electrostatics
1. Define the following terms
a. Electric field
b. Electric line of forces
c. Electric flux
d. Electric flux density
e. Electric field strength
2.
3.
4.
5.
6.
7.
8.
Explain permittivity? Define terms Absolute permittivity and Relative permittivity.
What you understand by dielectric strength and dielectric breakdown in capacitor.
Derive expression for the energy stored in capacitor (IMP)
State and explain how capacitance are classified on the basisof nature of dielectric used
Explain the charging process of a capacitor. (IMP)
What is capacitor ? Discuss the factor which affect the capacitance.
Obtain an Expression for capacitance of parallel plate capacitor with composite medium
of three materials . (IMP)
9. An initially uncharged capacitor in series with a resistor is connected to a dc supply at t =
0. Sketch the waveform of current and the voltage across the capacitor . State their
expression . Define the time constant. (IMP)
10. Explain Discharging of capacitor through a Resistance.
Numerical questions on Electrostatics
1. Two positive charges of 12 X 10-10C and 8 X 10-10 are placed 10 cm apart. Find the work
done in bringing two charge 4 cm closer. (ans- d1 = 0.1 m, d2= 6, w= 5.76x 10-8)
2. Two charges +5 X10-8 C and -3 X 10-8 C are 5 Cm apart. Find the work done needed to
move one charge s to infinity. ( Ans – d1 = 0.05m, d2= infinity, w = 2.7x10-4 J)
3. Find the work done in bringing a charge of +10 X 10-4 µC from infinity to a point 25cm
from a change of +3 X 10-2 µC. ( 1.08 MJ)
4. A capacitor of 50µF is uniformly charged with a current of 10mA for 10 Sec . Calculate
a) charge, b) capacitor voltage c) stored energy. ( ans 0.1 C, 2000v, 1000J)
5. Two flat parallel plates measuring 1 m X 2 m and separated by 10 cm are charged by
transferring 10-6 coulombs from one plate to other. The permittivity of the coil between
the plate is 2. Calculate a) Capacitance of parallel plate b) Potential difference between
the plate c) Electric field intensity d) electric flux density between the plates. (354.16 PF,
2823.582V, E=V/d= 28.235X103, 5x10-7 c/m2)
6. A capacitor consist of two parallel rectangular plates each 120 mm square separated by 1
mm in air. When a voltage of 1000 v is applied between the plates , calculate a) charge
on capacitor, b) the electric flux density c) electric field strength in
dielectric.(1.06214x10-9,8.854x10-6c/m2, E=D/Є0=1x 106 v/m
7. Two capacitor of 8µF and 2µF are connected in series across 400 v supply. Calculate a)
Resultant capacitance b) charge on each capacitor, c) P.D across each capacitor. (Ans
6.4x 10 -4, 1.6 micro F, v1 = 80 V, v2= 320V)
8. Three capacitors of value 2µF ,4µF and 6µF have applied voltage of 60 V across their
series combination. Determine the voltage on each capacitors.(v1= 32.72, v2=16.364v,
v3 =10.909)
9. Two capacitor are connected in parallel having equivalent capacitance of of two 10µF
while same capacitors when connected in series have equivalent capacitance of 2µF. find
the value of two capacitor.(c1 =7.236µF, c2=2.639 µF, C1= 2.639 µF c2 = 7.236µF
10. Three capacitor A,B, C have capacitance 20, 50 and25µF respectively. Calculate a)
Charge on each when connected in parallel to a 250 V supply b) Total capacitance c)
Potential difference across each when connected in series.(ans Qa = 5mC, Qb =12.5mC,
Ceq =9.090 µF, Va = 113.63V, Vb= 45.45V, Vc = 90.909V)
11. Two capacitor of 50µF each are connected in parallel with each other and this
combination is connected in series with two capacitors of 80µF and 40µF each. Calculate
equivalent capacitance of the circuit. (21.0526 µF)
12. Calculate the capacitance of an air insulated capacitor with 13 square plates each of 10
cm side, the distance between them being 2 mm. Assume medium to be air. (531 PF)
13. A parallel plate capacitor has the area of 10 Cm square between the plates is 0.1 cm. The
dielectric strength of the material between the plates is 0.1 cm. The dielectric strength of
the material between the plates is 40kV/cm and its dielectric constant is . 4Determine the
maximum energy in joules that the capacitor can store.( C = 35.416 PF, energy = 283.334
J)
14. A capacitor is made of two parallel plate with an area of 11 cm square and are separated
by mica sheet 2 mm thick . if for mica Єr = 6, find its capacitance . If now one plate of
capacitor is moved further to give an air gap of 0.5 mm wide between the plates and mica
find the value of capacitance.
15. An air condenser has an area of 100cm2 the plates being 4 mm apart. It is connected in
series with another condenser having a plate area of 20 cm2 , the plate being separated by
a dielectric of 0.1 mm thick with permittivity of 2.5. if the p.d. across air condenser is
1000 v, find the P.d across the second condenser. Find the energy stored in the
combination.
16. The 100µF capacitor is charged from 200 V supply. After it is fully charged and
immediately connected in parallel with 50µF capacitor . Calculate a) electrostatic energy
before the capacitor are connected in parallel b) electrostatic energy after the capacitor
are connected in parallel.
17. A 40µFcapacitor is charged to 50V. It is then connected in parallel with 60µF capacitor
charged to 40 V . Determine the voltage of the parallel combination and loss of energy
when a) plates of similar polarity are connected together b) when plates of opposite
polarity are together.
18. Two capacitors 0.2µF and 0.05µF are charged to a voltage of 100 V and 300 V
respectively. The capacitor are then connected in parallel by joining terminals of
corresponding polarity together. Calculate a) charge on each capacitor before being
connected in parallel, b) energy stored on each on each capacitor before being connected
in parallel, c) charge on equivalent capacitor after parallel connection , d) voltage across
equivalent capacitor.
19. A 2µF capacitor is connected by closing a switch to a supply of 100 volt through 1 Megh
ohm series resistor. Calculate a) Time constant b) initial charging current , c) the initial
rate of rise of voltage across capacitor , d) time taken for the capacitor voltage to reach 60
V and e) voltage across the capacitor 6 second after the switch has been closed..
20. A resistor of 2 meghaohm is connected in series with capacitor of 0.01 µF across dc
voltage source of 50 v. Calculate a) capacitor voltage after 0.02s, 0.04s, 0.06s and 1 hour,
b) charging current after 0.02 s, 0.04s, 0.06s and 0,1s.
21. When a dc voltage is applied to a capacitor , thr voltage across its terminal is found to
build in accordance with Vc = 150(1- e-20t). After a lapse of 0.05s, the current flow equal
to 1.14 m A. Find a) value of capacitance , b) Energy stored in this time.
22. A capacitor is charged to 15 V. If a source of 30 V Dc is applied to the capacitor
through a resistor of 100 Kilo ohm, tending to charge it further to more than 15 v,
determine the time taken for the capacitor to change to 25 v after application of the
voltage. The capacitor has a value0f 100 µF
23. 5 µF capacitor is connected to a constant voltage source through a resister of 2 mega
ohm. Calculate the time taken for the capacitor to lose a ) 50% b) 95%, when the voltage
sourse is short circuited.
24. A capacitor of 2 µF capacitance charged to potential difference of 200 v Is discharged
through a resister of 2 mega ohm . calculate a) the initial value of discharge current, b) its
value 4 Sec later, c) initial decay of the capacitor voltage.
Numerical Questions on Transformer
1) A single phase 50 Hz transformer has 80 turns on the primary winding and 280 turns in
the secondary winding. The voltage applied across the primary winding is 240 V at 50
Hz. Calculate
a) Maximum flux density in the core
b) Induced emf in the secondary
The net cross-sectional area of the core is 200 cm2 (ans- Bm =0.68 wb/m2, E2 = 840V)
2) A 10 KVA , 3300/240 V , single phase , 50 Hz, transformer has a core area of 300 cm
squ. The flux density is 1.3 tesla. Calculate
a) Number of primary turns
b) Number of secondary turns
c) Primary full load current. (ans – 382, 28,3.03)
3) For a single phase transformer having primary and secondary turns of 440 and 880
respectively , determine the transformer kVA rating if half load secondary current is 7.5
A and maximum value of core flux is 2.25 mWb. (ans- 6.5934KVA)
4) A 250 kVA 50 Hz single phase transformer has ratio of secondary to primary turns as 0.1.
The secondary voltage at no load condition is 240 V. Calculate
a) Primary voltage
b) Full load primary and secondary currents. (ans -2400 V, I1 = 104.1 A, I2 = 1041.6)
No load Losses questions
5) A 50 kVA 2300/230 V , 50 Hz transformer takes 200 watts and 0.3 A at no load , when
2300 V are applied to the high voltagre side. The primary resistance is 3.5 ohm.
Determine
a) Core losses and
b) no load PF (199.68 W, Cosфo= 0.291 lag)
6) A single phase transformer has a primary voltage of 230 V. No load primary current is 5
A . No load pf is 0.25. number of primary turns are 200 and frequency is 50 Hz calculate
a) Maximum value of flux in the core
b) Core losses
c) Magnetizing current. (Ans- фm = 5.18mwb, 287.5 W, 4.85A)
Equivalent Resistance Transformer
7) A single phase transformer c turn ratio n1:n2 of 4. If a 50 ohm resistance is connected
across secondary. What is resistance referred to primary? (ans ¼)
8) A resistance is connected across secondary of an ideal transformer has a value of 800
ohm as referred to the primary. The same resistance when connected across the primary
has a value 3.125 ohm as referred to secondary. Find the ratio of transformer.( ans 0.25)
9) A 6600/400 V transformer has a primary resistance of 2.5 ohm and a reactance of 3.9
ohm . the secondary resistance is .01 ohm and the reactance is 0.025 ohm. Determine the
equivalent circuit parameter referred to primary and secondary. ( R01 = 5.28, X01 =
10.84,R02 = 0.02, X02 = .04)
10) A 50 KVA 4400/220 V transformer has R1 = 3.45 ohm, R2 = 0.009 ohm. The reactance
are X1 = 5.2 ohm and X2 =0.015 Calculate for transformer
a) Full load current on primary and secondary side
b) Equivalent resistance , reactance impedance referred to primary side and secondary
side
c) Total copper loss using individual resistance and equivalent resistance. (I1 = 11.36
A, I2=227.27 A, R01 = 7.05, X01 = 11.2, Z01 =13.23, R02 = 0.02, X02 = 0.028, Z02 =
0.03)
Regulation
11) A 200 kVA, 2200/440 V, 50 Hz, single phase transformer is operating at full load, 0.8
lagging pf. The voltage on secondary of the transformer at full load, 0.8 lagging pf is
400V. Calculate voltage regulation of the transformer. (Ans – 9.09)
12) A single phase, 440/220 V, 10 kVA, 50 Hz transformer has a resistance of 0.2 ohm and
reactance of 0.6 ohm on h.v.side. The corresponding values of l.v side are 0.04 ohm and
0.14 ohm. Calculate the percentage regulation on full load for (i) 0.8 lagging P.F (ii)
0.8leading P.F (iii) unity P.F (Ans R02 = 0.09, X02 =0.29, i) 5.08% ii) 2.11%, iii) 1.86%)
13) Calculate the regulation of a transformer in which resistive drop is 1% of the output and
reactive drop is 5 % of the output, when the pf is (a) 0.8 lagging, (b) unity, and (c) 0.8
leading. (Ans a) 3.8% b) 1 % c) -22%
14) A 230/460 V transformer has a primary resistance of 0.2 ohm and a reactance of 0.5 ohm
and the corresponding values for the secondary are 0.75 ohm and 1.8 ohm respectively.
Find the secondary terminal voltage when 10 A is supplied at 0.8 p.f lagging. (Ans 424.8
V)
Efficiency
15) Iron loss of 80 kVA, 1000/250V, Single Phase, 50 Hz, transformer is 500 W. The copper
loss when the primary carries a current of 50A is 400 W. Find (i) area of cross section of
limb if working flux density is 1 T and there are 1000 turns on the primary, (ii) efficiency
at full load and pf 0.8 lagging and (iii) efficiency at 75% of full load and unity pf. (ans i)
4.5 x 10 -3 ii) 98.61% iii) 98.81%)
16) A 100 kVA, Single phase transformer has iron loss of 600 W and copper loss of 1.5 kW
at full load current. Calculate the efficiency at (i) full load and 0.8 lagging pf, and (ii) half
load and unity pf (Ans i) 97.44% ii) 98.09%)
17) A 600 kVA, single phase transformer has an efficiency of 92% at full load and also at
half load, working at unity pf. Calculate the efficiency of the efficiency of the transformer
at 60% full load and unity pf. ( ans Wcu = 34.8 KW, Wi = 17.4 , 92.32%)
18) A 100 kVA, single phase transformer has an efficiency of 97% at full load and 0.8
lagging pf, calculate (i) iron loss, (ii) full load copper loss and (iii) maximum efficiency. (
Ans i) 0.965KW, Wcu =1.58KW, 97.07%)
Unit 4
Question on AC fundamental
1. Define with respect to alternating quantity
a. Cycle
b. Waveform
c. Amplitude
d. Periodic Time
e. Frequency
2. Define form factor and peak factor as related with AC supply
3. Define average value and rms value of sinusoidal varying quantity and hence derive the
expression for each in terms of their peak value.
4. Explain the concept of phase and phase difference in alternating quantity.
5. Define following terms and hence state their unit
a. Active power
b. Reactive power
c. Conductance
d. Susceptance
e. Admittance
6. Derive an expression for instantaneous current and power consumed when voltage of V =
Vm sinwt is applied through pure inductance alone. (imp)
7. Prove that the current in purely capacitive circuit leads the voltage by 900 and current in
purely inductive circuit lags applied voltage by 900.
8. Prove that voltage and current in purely resistive circuit are in phase.
9. Show that the average power consumed by inductor is zero.
10. Explain the concept of inductive and capacitive reactance. How it depends on the
frequency.
Numerical questions on AC fundamental
1. At t = 0, the instantaneous value of a 60 Hz sinusoidal current is +5 ampere and increases
in magnitude further. Its rms value is 10A
a. Write the expression for its instantaneous value
b. Find the current at t = 0.01 and t = 0.015 second
c. Sketch the waveform indicating these value.
(Ans: Imax = 14.14, ф = 20.7, it0.01 = -11.8 A, it0.015 = -3.31)
2. An alternating current varying sinusoidal at 50 Hz has its rms value of 10 A. write the
equation for its instantaneous value and find its value at a) .0025sec after passing through
positive maximum value and b) 0.005 sec after passing the zero and increasing
negatively. ( Ans Imax = 14.14, a) 10 A, b) -10 A)
3. A 60 Hz sinusoidal current has an instantaneous value at 7.07 at t = 0 and rms value and
rms value of 10√2 Amp. Assuming current wave to enter positive half wave at t = o ,
determine
a) expression for instantaneous current
b)magnitude of current at t = 0.0125 sec
c) magnitude of current at t = 0.025 sec after t = 0.
(ans Imax = 20 A, ф = 20.7o b) -18.7 A c)-13.227A)
4. The wave form of a voltage has a form factor of 1.15 and a peak factor of 1.5. If the
maximum value of the voltage is 4500 V, calculate the average value and rms value of
the voltage. (Ans Vrms = 3000v, Vavg = 2608.7 V)
5. A circuit consist of three parallel branches. The branch current are given as i1 = 10 sinwt,
i2 = 20 sin(wt+ 60 o ) and i3 = 7.5 sin (wt- 30o ). Find the resultant current and expression
it in the form i = Im sin (wt +ф). If supply frequency is 50 Hz , calculate the resultant
current when a) t = 0 b) t = 0.001 S. ( Ans i =29.76 sin (wt + 27.23 o ), 13.5A, 21.09A)
6. A sinusoid ally varying alternating current has rms value of 20 A and periodic time of 20
milli second. If the wave form of this current enters into its positive half cycle at t = 0,
find the instantaneous value of the current at t1 = 6 millisecond and t2 = 12 milliseconds (
Ans i = 26.89A, -16.62A)
7. The instantaneous current is given by i = 7.071sin (157.08 t – π/4). Find its effective
value, periodic time and the instant at which it reaches its positive value, sketch the
waveform from t = 0 over one complete cycle. (Ans 5 A, 40 ms, 0.01499 sec)
8. An ac circuit consist of a pure resistance of 10 ohm and is connected across an ac supply
of 230 V, 50 Hz calculate a) current b) power consumed c) equation for voltage and
current, (Ans 23A,5290 W, )
9. A resistive heating element is designed for 240 V, 60 Hz. Calculate its power if its
resistance is 28.8 ohm. How will it perform if it is connected to a 240 V dc sources? (Ans
2Kw)
10. A pure inductive coil allows a current of 10 A to flow from 230 V , 50 Hz supply .Find a)
inductive reactance, b) inductance of the coil c) power absorbed. (Ans 23 ohm, 0.03 H,
zero)
11. The ac voltage across a 0.01 Micro farad capacitor is 240 sin (1.25 x 10 4t - 30o). write
mathematical expression for current through it. (ans – 0.03sin (1.25 x 10 4t + 60o)A)
Unit 5
Single Phase AC Circuits and Polyphase AC Circuits
1. Derive and show the waveforms of voltage, current and power for R-L series circuit when
supplied by a voltage v(t) = Vm sin wt. Draw phasor diagram.
2. Draw power triangle and define active power , reactive power and apparent power. Also define
power factor.
3. Derive and show the waveforms of voltage, current and power for R-C series circuit when
supplied by a voltage v(t) = Vm sin wt . Draw phasor diagram.
4. Sketch and explain the phasor diagram of RLC series circuit for i) XC>XL (ii) XC<XL (iii) XC =
XL.
5. What is admittance? Which are its two components? State its unit. How the admittance is
expressed in rectangular and polar form. Also Define Conductance and Susceptance. Draw the
admittance triangle and explain.
6. What is resonance in series circuit? State the characteristics of series resonance.
7. Derive the equation for the resonant frequency in series RLC circuit?
8. Define bandwidth of series RLC circuit. Derive the expression for half power frequencies for
series resonance.
9. Define quality factor of series RLC circuit and obtain expression for it?
10. What is three phase system? State the various advantages of three phase system over single phase
system.
11. Define (i) symmetrical system (ii) phase sequence (iii) balanced load (iv) unbalanced load (v)
Phase voltage (vi) Phase current (vii) Line voltage (viii) Line current
12. Derive the relation between line and phase values of currents and voltages for balanced three
phase star connected load connected across three phase a.c. supply. Derive also power consumed
by the load.
13. Derive the relation between line and phase values of currents and voltages for balanced three
phase delta connected load connected across three phase a.c. supply. Derive also power consumed
by the load.
14. State the equations for real power, apparent power and reactive power for three phase balanced
load.
15. An alternating voltage of 80 +j60 V is applied to a circuit and the current flowing is 4-j2 A. Find
the (i) impedance (ii) Phase angle (iii) power factor (iv) Power Consumed.
(Ans: Z = 22.37 Ω, ϕ = 63.430, pf= 0.447 (lagging) , P= 199.81 W)
16. When a sinusoidal voltage of 120 V (rms) is applied to a series R-L circuit, it is found that there
occurs a power dissipation of 1200w and a current flow given by i(t) = 28.3 sin(314t-ϕ). Find the
circuit resistance and inductance.
( Ans: R= 3 Ω, L= 0.0165 H)
17. A series circuit consists of a non- inductive resistance of 6 Ω and an inductive reactance of 10 Ω
when connected to a single-phase ac supply, it draws a current i(t) = 27.89 sin(628t -45o).
Calculate (i) the voltage applied to the series circuit in the form of Vm sin(wt ± ϕ) , (ii)
inductance, and (iii) power drawn by the circuit.
(Ans: v = 325.2 sin(wt + 14.040), L = 15.9 mH, P= 2332.78 W)
18. When an inductive coil is connected to a dc supply at 240 v, the current in it is 16 A. When the
same coil is connected to an ac supply at 240 V, 50 Hz, the current is 12.27 A. calculate (i)
resistance, (ii) impedance (iii) reactance (iv)inductance of coil.
(Ans: R = 15 Ω, Z = 19.56 Ω, XL = 12.55 Ω, L = 0.04 H)
19. A coil connected across a 250 V, 50 Hz supply takes a current of 10 A at 0.8 lagging PF. What
will be the power taken by the choke coil when connected across a 200 V, 265 Hz supply? Also
calculate resistance and inductance of the coil.
(Ans: R= 20Ω, L = 0.0477 H, P= 1.753 kW)
20. A load of 22 kW operates at 0.8 lagging pf when connected to a 420 V, single phase , 50 Hz
source , Find (i) current in the load (ii) power factor angle (iii) impedance (iv) resistance of load
(v) reactance of load, (vi) voltage and current equations
(Ans: I = 65.48 A, ϕ = 36.870, Z = 6.41 Ω, R = 5.13 Ω, XL = 3.85 Ω, v = 593.97 sin100πt, i =
92.6 sin (100πt – 36.870)
21. A capacitor of 35 µF is connected in series with a variable resistor. The circuit is connected
across 50 Hz mains. Find the value of the resistor for a condition when the voltage across the
capacitor is half the supply voltage.
(Ans: R = 157.5 Ω)
22. A voltage of 125 V at 50 Hz is applied across a non-inductive resistor connected in series with a
capacitor. The current is 2.2 A. The power loss in the resistor is 96.8 W. Calculate the resistance
and capacitance. (Ans: R = 20Ω, C = 59.85 µF)
23. A resistor and capacitor are connected across a 250 V supply frequency is 50 Hz, the current
drawn is 5 A. when the frequency is increased to 60 Hz, it draws 5.8 A. Find the values of R and
C and power drawn in the second case.
(Ans: R= 19.96 Ω, C = 69.4 µF, P2 = 671.45 W)
24. A resistor of 20 Ω, inductor of 0.05 H and capacitor of 50 µF are connected in series. A supply
voltage of 230 V, 50 Hz is connected across the series combination. Calculate the following: (i)
impedance (ii) current drawn by the circuit (iii) phase difference and power factor and (iv) active
and reactive power consumed by the circuit.
(Ans: Z = 51.95 Ω, ϕ = 67.360, I = 4.43 A, pf = 0.385(lagging), P = 392.28 W, Q= 940.39
VAR)
25. A circuit consists of a pure inductor, a pure resistor and a capacitor connected in series. When the
circuit is supplied with 100 V, 50 Hz supply, the voltages across inductor and resistor are 240 V
and 90 V respectively. If the circuit takes a 10 A leading current, calculate (i) value of
inductance, resistance and capacitance, (ii) power factor of the circuit, and (iii) voltage across the
capacitor. ( Ans : R = 9 Ω, L = 0.076 H, C = 112.24 µF, Pf = 0.9 (leading), Vc = 283.6 V )
26. Two impedances Z1 = 40 < 300 Ω and Z2 = 30 < 600 Ω are connected in series across a single
phase 230 V, 50 Hz supply. Calculate the (i) current drawn (ii) pf (iii) power consumed by the
circuit. (Ans: I = 3.4 A, pf = 0.734 (lagging), P = 573.99 Ω)
27. A coil having a resistance of 50 Ω and an inductance of 0.02 H is connected in parallel with a
capacitor of 25 µF across a single phase 200 V, 50 Hz supply. Calculate the current in coil and
capacitance. Calculate also the total current drawn, total pf and total power consumed by the
circuit. (Ans: I = 4.08 <15.270 A, pf = 0.965 (lagging), P = 787.44 W)
28. Two impedances Z1 = 30 < 450 Ω and Z2 = 45 < 300 Ω are connected in parallel across a single
phase 230 V, 50 Hz supply. Calculate (i) current drawn by each branch, (ii) total current, (iii)
overall pf. Also draw the phasor diagram indicating the current drawn by each branch and total
current, taking the supply voltage as reference.
(Ans: I1 = 7.67 < -450 A, I2 = 5.11 < -300 A, I = 12.67 < -39.010 A, pf = 0.777 (lagging))
29. Two circuits, the impedances of which are given by Z1 = (10 + j15) Ω and Z2 = (6- j8) Ω are
connected in parallel across an ac supply. If the total current supplied is 15 A, what is the power
taken by each branch? (Ans: P1 = 737.88 W, P2 = 1437.78 W)
30. A circuit consists of a 25 Ω resistor; 64 mH inductor and 80 µF capacitor connected in parallel
across a 110 V, 50 Hz single phase supply. Calculate the individual currents drawn by each
element, the total current drawn from the supply and the overall pf of the circuit. Draw the phasor
diagram. (Ans: IR = 4.4 < 00, IL = 5.47 < -900, IC = 2.76 < 900, I = 5.17 < -31.630, PF = 0.851
(lagging).
31. An ac circuit connected across a 200 V, 50 Hz supply has two parallel branches A and B. Branch
A draws a current of 4 A at 0.8 lagging pf, while the total current drawn by the parallel
combination is 5 A at Unity PF. Find (i) current and PF of branch B, and (ii) admittances of
branches A and B , and their parallel combination both in polar and rectangular forms. (Ans: IB =
3 < 53.130 A, PFB = 0.6 (leading) , YA = 0.02 <-36.870 Ʊ, YB = 0.015 < 53.130 Ʊ, Y = 0.025 < 00
Ʊ)
32. Two circuits A and B are connected in parallel to a 115 V,50 Hz supply. The total current taken
by the combination is 10 A at unity PF. Circuit A consists of a 10 Ω resistor and 200 µF capacitor
connected in series. Circuit B consists of a resistor and inductor in series. Determine (i) current
(ii) power factor (iii) impedance (iv) resistance, and (v) reactance of the circuit B . (Ans : IB =
8.5 < -37.540 A , PFB = 0.79 ( lagging) , ZB = 10.73 + j 8.24 Ω, RB = 10.73 Ω, XB = 8.24 Ω )
33. Two impedances R1 – j XC1 and R2 + j XL2 are connected in parallel across a supply voltage v =
100√2 sin 314t. The current flowing through two impedances are i1 = 10√2 sin ( 314t + (π/4))
and i2 = 10√2 sin ( 314t - (π/4)) respectively. Find the equation for instantaneous value of total
current drawn from the supply. Also find values of R1, R2, Xc1 and XL2. (Ans: i = 20 sin 314t, R1
= 7.07 Ω, R2 = 7.07 Ω, Xc1 = 7.07 Ω, XL2 = 7.07 Ω)
34. A series RLC circuit has the following parameter values: R = 10 Ω, L = 0.01 H, C = 100 µF.
Compute the resonant frequency , bandwidth, and lower and upper frequencies of the bandwidth.
(Ans: f0= 159.15 Hz, BW = 159.15 Hz, f1 = 79.58 Hz, f2 = 238.73 Hz)
35. An RLC series circuit with a resistance of 10 Ω, inductance of 0.2 H and a capacitance of 40 µF
is supplied with a 100 V supply at variable frequency . Find the following w.r.t the series resonant
circuit: (i) frequency at which resonance takes place (ii) current (iii) power (iv) power factor (v)
Voltages across R-L-C at that time (vi) quality factor (vii) half power points (viii) resonance and
phasor diagrams
(Ans: f0 = 56.3 Hz, I0 =10 A , P0 = 100 W, PF = 1, VR0 = 100 V, VL0 = 707.5 V, VC0 = 707.5 V,
Q = 7.07, f1 = 52.32 Hz, f2 = 60.3 Hz)
36. The three equal impedances of each of 10< 600 Ω, are connected in star across a three-phase, 400
V, 50 Hz supply. Calculate the (i) line voltage and phase voltage (ii) power factor and active
power consumed , (iii) if the same three impedances are connected in delta to the same source of
supply, what is the active power consumed?
(Ans: VL = 400 V, Vph = 230.94 V , PStar = 8 kW, PDelta = 24 kW)
37. A balanced star-connected load is supplied from a symmetrical three phase 400 volts, 50 Hz
system. The current in each phase is 30A lags 300 behind the phase voltage. Find the (i) phase
voltage (ii) resistance and reactance per phase (iii) load inductance per phase, and (iv) total
power consumed. (Ans: Vph = 230.94 V, Rph = 6.67 Ω, Xph = 3.85 Ω, Lph = 0.01225 H, P = 18
kW)
38. A symmetrical three phase 400 V system supplies a basic load of 0.8 lagging power factor and is
connected in star. If the line current is 34.64 A, find (i) impedance (ii) resistance and reactance
per phase (iii) total power and (iv) total reactive volt amperes.
(Ans: Zph = 6.67 Ω , Rph = 5.33 Ω Xph = 4 Ω, P = 19.19 kW, Q = 14.4 kVAR)
39. A balanced star connected load is supplied by a 415 V, 50 Hz three phase system. Current in each
phase is 20 A and lags 300 behind its phase voltages. Find the (i) phase voltage (ii) power and
(iii) circuit parameters. Also, find power consumed when the same load is connected in delta
across the same supply. (Ans: Vph = 239.6 V, P = 12.45 kW, Zph = 11.98 Ω, Rph = 10.37 Ω, Xph
= 6 Ω, Lph = 19.1 mH, P∆ = 37.35 kW )
UNIT 6 – DC CIRCUITS
1. Classify and explain Electrical networks.
2. Explain the significance of the terms ‘active’, ‘passive’, ‘linear’, ‘non linear’, unilateral’,
‘bilateral’ with reference to the DC resistive network. Differentiate between ideal and
practical voltage and current sources.
3. Explain the conversion of voltage source into current source and vice versa and explain,
ideal and practical voltage sources and ideal and practical current sources.
4. State and explain the KCL and KVL (Kirchhoff’s laws)with suitable examples.
5. Derive an expression for conversion for star to delta network and delta to star network
conversion.
6. State whether the star – delta transformation is valid for balanced and /or unbalanced
networks equally? How?
7. With a suitable example, state and explain superposition theorem.
8. State and explain Thevenin’s theorem with one example.
9. Calculate the current through 2 ohm resistor and currents drawn from each battery.(ANS50A,0A,40A,10A)
10. Find the currents in 8 ohm resistor. (ANS- 5A each
)
11. Calculate the power loss in the load resistance R=1 ohm, using Superposition theorem
and Thevenin’s theorem. Determine the value of resistance which will absorb the greatest
power from the circuit when connected in place of 1 ohm resistor, also determine this
power.
(ANS- 195.9W,0.667ohm,204W )
12. Write the equations for the loops marked I and II using Kirchoff’s laws. Solve the
equations and determine the current in each of the voltage source. (ANS- 20V-1A,30V2A,10V-3A )
13. Calculate the power output of voltage source and voltage across terminals A and B.
(ANS- 24.42W,0.2325V)
14. By using loop analysis, find currents I1 ,I2 ,I3 and determine power output of each voltage
source. (ANS-0.3714A,-0.2286A,-0.2858A,3.714W,1.143W,1.429W)
15. Find the current in 5 ohm resistor by nodal analysis. (ANS- 0.468A
)
16. Estimate the equivalent resistance between terminals X and Y. (ANS-30Ohm)
17. Find the equivalent resistance between terminals A and B. (ANS-3.75Ohm)
18. Find the current flowing through 10 ohm resistor by using Thevenin’s theorem. (ANS0.32A)
19. Calculate the value of current in 30 ohm resistor connected between A and B by
Superposition theorem and Thevenin’s theorem. (ANS-0.583A)
20. Calculate the current flowing through 1 ohm load resistance by Superposition theorem
and Thevenin’s theorem. (ANS-14A)
21. Find the current flowing through 2 ohm load resistance (between terminals A and B) by
Superposition theorem and Thevenin’s theorem. (ANS-0.705A)
22. State and Explain superposition theorem as applied to simple D.C. circuitsQ.3] State formula
to convert the star connected network into its equivalent delta connected network.
23. State and explain Maximum power transfer theorem.
24. Classify and explain Electrical networks.
25. State and explain thevenin’s theorem
26. Derive the formulae to convert star connected network into its equivalent delta connected
network.Hence verify your results by thevenin’s theorem. All the resistances are in Ohm.
27. Explain the flowing terms with reference to DC resistive networks
a) Unilateral and Bilateral Networks
b) Linear Networks
c) Active and Passive Networks