MODULE 5 CIRCUIT PHASORS: RL AND RC CIRCUIT
5.1 Series R-L
Formulas:
Impedance
𝑍 = √𝑅 2 + 𝑋𝐿2
Voltage
VR = IRR
VL= ILXL
𝑉𝑇 = √𝑉𝑅2 + 𝑉𝐿2
Current
IT = I R = I L
V = I TZ
Impedance coil
A coil of wire designed to provide impedance in an electric circuit.
𝑍 = √𝑅 2 + 𝑋𝐿2
5.2 Parallel R-L
Formulas
Impedance
1
Current
1
1
= √𝑅 2 + 𝑋
𝑍
𝐿
2
𝐼𝑇 = √𝐼𝑅2 + 𝐼𝐿2
Voltage
VT = VR = VL
5.3 Series R-C
Formulas
Impedance
𝑍 = √𝑅 2 + 𝑋𝐶2
Voltage
Current
𝑉𝑇 = √𝑉𝑅 2 + 𝑉𝐶2
IT = I R = I C
V = IZ
Note that the IXc phasor is downward, exactly opposite from IXL phasor because of the
opposite phase angle.
5.4 Parallel R-C
Formulas
Impedance
1
1
1
= √𝑅 2 + 𝑋
𝑍
𝐶
2
Current
Voltage
𝐼𝑇 = √𝐼𝑅2 + 𝐼𝐶2
VT = VR = VC
Sample Problems
1) If a 50-Ω R and 70-Ω XL are in series with 120V applied. Find the impedance,
total current, power factor, and voltage across inductor and resistor.
2) A 500-Ω R is in parallel with 300-Ω XL with 500V. Find IT, pf, ZT.
3) A coil has a resistance of 35-Ω and an inductance of 0.14H the coil is connected
to 60cps, 117V power source. Calculate a)the circuit current b)phase angle
c)power used in the external circuit.
4) An impedance coil has a resistance of 20Ω and an inductive reactance of 40Ω.
For what value of series resistance with overall power factor of the circuit be 0.6
5) What should be the capacitance of a capacitor in series with a 250Ω resistor that
will limit the current to 1.2 amp when the circuit is connected to a 600V 60cycle
source. Calculate also the power factor in this condition.
6) A 15Ω R is in parallel with 20-Ω capacitor are placed 120V ac line. Find IR,IC, IT,
pf, ZT.
Self-Assessment Problems
1) A small ac motor used in washing machine is in effect, an RL circuit. If the
machine takes 311 watts and 4.5 amp from a 115volt source when operating
normally, calculate its power factor.
2) A 240 Volt 60cycle source is connected to a coil of wire that has a resistance of
75Ω and an inductance of 0.0477 Henry. Calculate the following. a)impedance
b)current c)power d) power factor
3) A resistor, in series with a 138μf capacitor is connected to a 60cycle source. If
the voltage drop across the capacitor is 115 volts and the power taken by the
circuit is 922 watts. Calculate a)the circuit current b)the ohmic value of resistor c)
the line voltage d) the circuit power factor.
MODULE 6 CIRCUIT PHASORS: RLC
6.1 Series R-L-C Circuit
Voltage
VT = VR + jVL – jVC
Impedance(Z Magnitude only)
If (XL > XC)
𝑍 = √𝑅 2 + (𝑋𝐿 − 𝑋𝐶 )2
Current
IT = I R = I L = I C
If (XC > XL)
𝑍 = √𝑅 2 + (𝑋𝐶 − 𝑋𝐿 )2
6.2 Parallel R-L-C Circuit
Voltage
VT = VR = VL = VC
Impedance
𝑍𝑇 =
𝑉𝑇
𝐼𝑇
Current
IT = IR + jIC - jIL
Sample Problems
1)
A coil of resistance 5 Ω and inductance 120 mH in series with a 100 μF
capacitor, is connected to a 300 V, 50 Hz supply. Calculate (a) the current
flowing, (b) the phase difference between the supply voltage and current, (c)
the voltage across the coil and (d) the voltage across the capacitor.
2)
A 30 Ω resistor , a 40 Ω inductive reactance, and a 60 Ω capacitive reactance
are connected in parallel across a 120-V 60Hz ac line. Find IT, phase angle,
ZT and Power.
3)
A resistance of 20 Ω, an inductance of 0.2H and a capacitance of 100μF are
connected in series across 220-V 50 Hz mains. Determine the following: a)
impedance b) current c) voltage across R, L, and C d) power in watts and VA
e) power factor and angle of lag.
Self-Assessment Problems
1)
A 130-V 200Hz power supply is connected across a 10 kΩ resistor , 0.05-μF
capacitor, and a 10-H coil in series. Find XL,XC,Z, θ, I, and P
2)
A 30-Ω resistor, a 15-Ω inductive reactance, and a 12-Ω capacitive reactance
are connected in parallel across a 120-V 60-Hz line. Find (a) the phasor
branch currents, (b) total current and phase angle, (c) impedance, and (d)
power drawn by the circuit.