TUTORIAL SHEET NO:-1
TOPIC: - SINGLE PHASE AC CIRCUITS
1) An alternating voltage is represented by the following expression v = 25 sin (200  t)
Calculate the following:- (i) Amplitude (ii) Time Period (iii) Frequency (iv) Angular
velocity (v) Form Factor (vi) Crest Factor (page 3-15, ex. 3.10.1, JSK)
2) Find the R.M.S. value, average value and form factor of the voltage waveform shown in
figure. (page 3-20,ex. 3.10.8, JSK)
Voltage
100V
0





1 cycle
3) Find the r.m.s. value of the resultant current in a wire carrying simultaneously a direct
current 10 A and a sinusoidal alternating current of peak value of 10 A.(page 3-21,
ex.3.10.10, JSK)
4) Draw the waveforms & phasor diagrams for the expression given below. (page 3-32,ex.
3.12.6, JSK)
i) v = 100 sin ( 314 t +  /3 ) volts
ii) i = 10 sin (314 t -  /2 ) amp
5) An alternating voltage is given by v= 141.4 sin(314t) .Find
(i) Frequency (ii) RMS value (iii) Average value
(iv) the instantaneous value of voltage when‘t’ is 3 msec.
(v) the time taken for the voltage to reach 100V for the first time after passing through
zero value. (page 3-46, ex. 3.15.10, JSK)
-1-
6) The instantaneous value of emf is V =300 sin (80t). Determine:(i) Average value (ii) RMS value (iii) Frequency (iv) Period (v) Angular Frequency (vi)
Amplitude (vii) Instantaneous value of emf at t = 0.1 sec. (page 3.21, ex. 3.9, SYS)
7) An alternating current is given be the equation 28.28 sin (314t). Determine:(i) Maximum value (ii) RMS value
(iii)the radians through which its phasor has rotated in 0.01 sec.
(iv) Value of current after t = 0.01 sec. (page 3.28, ex. 3.17, SYS)
8) Alternating voltage and current are given be the following equations:

e  142 sin( 628t ) i  4 sin  628  
6

Find: - (i) Frequency (ii) Irms (iii) Erms (iv) Phase angle between e and i. (page 3.28, ex. 3.18,
SYS)
-2-
TUTORIAL SHEET NO:-2
TOPIC: - SINGLE PHASE AC CIRCUITS
1) A pure resistance of 12  is connected across a 240 V, 50 Hz supply. Calculate:(i) Current (ii) power consumed and (iii) Write down the equations for voltage and current.
(page 4.2, ex. 4.1, SYS)
2) A non-resistive inductance of 0.15 H is connected across an ac supply of 250 V, 60 Hz.
Determine: - (i) Inductive reactance (ii) RMS current (iii) Active power and (iv) Voltage
and current equations. (page 4.4, ex. 4.2, SYS)
3) A pure capacitance of 50 F is connected across a 50 Hz, 400 V supply.
Calculate: - (i) capacitive reactance (ii) circuit current (iii) reactive power (iv) obtain
equations of voltage and current. (page 4.6, ex. 4.3, SYS)
4) A sinusoidal 50 Hz current of maximum value of 100 A flows through a capacitor of 318
F capacitance. Calculate (i) the expression for instantaneous current
(ii) reactance of the capacitor
(iii)equation of applied emf
(iv) rms value of applied emf and current. (page 4.7, ex. 4.4, SYS, S/2001)
R-L Series Circuit
5) A voltage v (t) = 141.4 sin (314t +10°) is applied to a circuit and a steady current given
by i (t) =14.14 sin (314t - 20°) is found to flow through it. Determine:(i) the p.f. of the circuit
(ii) the power delivered to the circuit
(iii) Draw the phasor diagram. (page 4.9, ex. 4.6, SYS,S/2000)
6) A coil connected to a 250 V, 50 Hz sinusoidal supply takes a current of 10 A at a phase
angle of 30°. Calculate the resistance and inductance of coil and also power taken by the
coil. (page 4.13, ex. 4.11, SYS)
7) A choke coil connected across a 250 V, 50 Hz supply takes a current of 10 A at 0.8 pf.
lag. What will be the power taken by the choke when connected across a 220 V, 25 Hz
supply? (page 4.14, ex. 4.14, SYS)
8) A current of 5A flows through a non-inductive resistance in series with a choking coil
when supplied at 250V, 50 Hz. If voltage across the resistance is 125 V and across the
coil, 200V, Calculate :(i) impedance, reactance and resistance of the coil
(ii) power absorbed by the coil
(iii) total power
(iv) Also draw the phasor diagram. (page 4.16, ex. 4.16, SYS)
-3-
I=5A
VR=125V
V = 250V
f= 50 Hz
Vr
R
r
Vcoil =200V
VL
L
XL
-4-
TUTORIAL SHEET NO:-3
TOPIC: - SINGLE PHASE AC CIRCUITS
R-C Series Circuit
1) A voltage of 220 volts at 50 Hz is applied across a non-inductive resistor connected in
series with a condenser. The current in the circuit is 2.5 A. The power loss in the resistor
is 100 watts and that in the condenser is negligible. Calculate the resistance and
capacitance. (page 4.21, ex. 4.20, SYS)
2) A 240 V, 50 Hz series circuit takes rms current of 20 A. The maximum value of the
current occurs 1/900 second before the maximum value of voltage. Calculate: - (i) power
factor (ii) average power (iii) parameters of circuit. (page 4.22, ex. 4.21, SYS)
3) A resistor and capacitor are connected in series across a 150 V, ac supply. When the
frequency is 40 Hz, the current is 5A and when the frequency is 50 Hz, the current is 6A
Find (i) R (ii) C. (page 4.22, ex. 4.22, SYS)
R-L-C Series Circuit
4) A series R-L-C circuit consists of R = 10 , L= 0.318 H, C = 63.6 F and emf source e(t)
= 100 sin 314t. Calculate :i) Expression for i(t)
ii) Phase angle between voltage and current
iii) Power factor
iv) Active power consumed
v) Draw the phasor diagram. (page 4.32, ex. 4.24, SYS)
5) A coil of power factor 0.6 is in series with a 100 F capacitor. When connected to a 50
Hz supply, the voltage across to coil is equal to voltage across capacitor. Find the
resistance and inductance of the coil. (page 4.33, ex. 4.25, SYS,S/1999)
6) A 230 V,50 Hz voltage is applied to a coil of L = 5 mH and R = 2  in series with a
capacitance C. What value must C have so that the p.d. across the coil shall be 250V?
(page 4.39, ex. 4.30, SYS)
7) A series circuit having a resistance of 10 , an inductance of 0.025 H and a variable
capacitance is connected to a 100 V, 25 Hz single phase supply, the current drawn being 8
A. Calculate:(i) Capacitance (ii) Impedance (iii) power factor (iv) power consumed (v) Sketch the
phasor diagram. (page 4.41, ex. 4.33, SYS)
I = 8 Amp R= 10 
L= 0.025H
V =100 V
f = 50 Hz
-5-
C
R-L-C Series Resonance Circuit
8) A pure capacitor is connected in series with practical inductor (coil). The voltage source
is of 10 volts, 10,000 Hz. It was observed that the maximum current of 2A flows in the
circuit when the value of capacitor is 1 F. Find the parameters (R and L) of the coil.
(page 4.45, ex. 4.35, SYS,W/2002)
Imax = 2 Amp
R
L
V =240 V
f = 10,000 Hz
-6-
C= 1µF
TUTORIAL SHEET NO:-4
TOPIC: - SINGLE PHASE AC CIRCUITS
R-L-C Series Resonance Circuit
1) An inductive coil having resistance of 20  and inductance of 0.1 H is connected in series
with 10 F capacitor. The combined circuit is energized from 200V, variable frequency
supply. Calculate:(i) condition for which the current will be maximum in the circuit
(ii) voltage across the coil
(iii) power factor of the coil. (page 4.46, ex. 4.36, SYS, W/2001)
2) A circuit having a resistance of 5, an inductance of 0.4 H and a variable capacitance in
series, is connected across a 110 V, 50 Hz supply. Calculate:(i) the value of capacitance to give resonance
(ii) current
(iii) voltage across the capacitance (page 4.46, ex. 4.37, SYS,S/2001)
I
R= 5 
L = 0.4 H
C
V = 110 V
f = 50 Hz
3) A large coil of inductance 1.405 H and resistance 40  is connected in series with a
capacitor of 2 F. Calculate the frequency at which the circuit resonates. If a voltage of 100
V is applied to the circuit at resonant condition, calculate the current drawn from the supply
and the voltage across the coil and the capacitor. (page 4.47, ex. 4.38, SYS,W/1999)
R-L-C Parallel Circuit
4) Two impedances Z1 = (6+j8)  and Z2 = (8-j6)  are connected in parallel across 100 V
supply. Determine:(i) current and power factor for each branch
(ii) overall current and power-factor
(iii) power consumed by each branch and total power. (page 4.57, ex. 4.45, SYS, W/2003)
I
I1
I2
6 
8 
8
6
V = 100 V
-7-
5) Two impedance Z1 = (10+j15)  and Z2 = (40-j60)  are connected in parallel across ‘V’
volts. Find out parameters of the simplest series circuit which when connected to same
source would draw same current at same power factor. (page 4.59, ex. 4.47, SYS)
6) Two impedance Z1 = (8+j6)  and Z2 = (3-j4)  in parallel. If the total current of this
combination is 25A, find the current taken and power consumed by each impedance. (page
4.65, ex. 4.55, SYS)
7) Two impedance Z1 = (10+j5)  and Z2 = (8-j6)  are connected in parallel and connected
across voltage of V = (200+j0). Calculate the branch currents and total current and power
factor of complete circuit. Draw phasor diagram. (page 4.66, ex. 4.57, SYS)
I
I1
I2
R1= 10 
R2= 8 
V = 200 V
XL2 = 6 
XL1 = 5 
-8-