Electrical Circuit (Phasor Diagram) Quizzes and Answer
Arya Bagas
Department of Energy
Problem 1:
If the voltage 𝑉1 = 12 Cos (60t + 45°)V is applied to a 50 Micro Farad capacitor,
determine the current flowing through the capacitor?
Solution 1:
1. Determine the parameter:
𝑉1 = 12 Cos (60t + 45°)V; C = 50 Micro Farad; ω = 60t; V = 12∟45°
2. Calculate the ω with capacity of capacitor:
(50x10−6 ) . (60𝐽) = 0,003J
3. Polarize the J0,003:
r = √𝑥 2 + 𝑦 2 = √02 + 0,0032 = 0,003
𝑦 0,003
θ = 𝑇𝑎𝑛−1 = 𝑇𝑎𝑛−1 ( ) = 90º
𝑥 0
4. Calculate the current:
I = V . JωC = (12∟45°) . (0,003∟90°) = 0,036∟135°A
5. Change to time form:
I(t) = 0,036 Cos (60t + 135°)
Problem 2:
If the source voltage Vs = 20 Sin (10t + 30º) V, is applied to a resistor with a
resistance of 4 Ohms and is placed in series with the inductor of 0.2 H. Determine
the voltage v(t) and current i(t) in the time domain, and prove that:
a. 8,944 sin (10t + 93,43) V
b. 4,472 Sin (10t + 3,43) A
Solution 2:
1. Determine the parameter:
V = 20∟30º ; ω = 10t ; Z = ?
2. Find Z value:
, Z = R + jωL = 4 + j10 . 0,2 = 4 + j2
3. Polarize the 4 + j2 value using r and θ:
r = √𝑥 2 + 𝑦 2 = √42 + 22 = √20 = 4,472
𝑦 2
θ = 𝑇𝑎𝑛−1 = 𝑇𝑎𝑛−1 ( ) = 26,57º
𝑥 4
4. Calculate the current:
𝑉𝑠 20∟30°
I= = = 4,472∟3,43°A
𝑍 4,472∟26,57°
5. Calculate the voltage:
V = I . jωL = (4,472∟3,43°) . (2∟90°) = 8,944∟93,43°V
6. Convert them into the time form:
I(t) = 4,472 Sin (10t + 3,43°)A
V(t) = 8,944 Sin (10t + 93,43°)V
Problem 3:
Prove that the capacitor voltage 𝑉0 (t) in the circuit below is 𝑉0 = 14.14 Cos (10t
- 35°)V, V= 20 Cos (10t + 100°).
Solution 3:
1. Determine the parameter:
1
V = 20 Cos (10t + 100°); ω = 10(t); C = 𝐹; V = 20∟100°;
20
2. Calculate 𝑍1 value:
1 1 1
𝑍1 = = 1 = 1 = -j2 Ohm
𝑗𝜔𝐿 𝑗10 . 𝑗
2 2
3. Calculate 𝑍2 value and find 𝑍3 :
𝑍2 = jωL = j10 . 0,5 = j5 Ohm- and 𝑍3 = 10 Ohm
4. Calculate the total of impedance:
𝑍𝑇 = (𝑍2 ||𝑍3 ) + 𝑍1 = (j5||10) + (-j2) = 2 + j2
5. Polarize the total of impedance using r and θ:
Arya Bagas
Department of Energy
Problem 1:
If the voltage 𝑉1 = 12 Cos (60t + 45°)V is applied to a 50 Micro Farad capacitor,
determine the current flowing through the capacitor?
Solution 1:
1. Determine the parameter:
𝑉1 = 12 Cos (60t + 45°)V; C = 50 Micro Farad; ω = 60t; V = 12∟45°
2. Calculate the ω with capacity of capacitor:
(50x10−6 ) . (60𝐽) = 0,003J
3. Polarize the J0,003:
r = √𝑥 2 + 𝑦 2 = √02 + 0,0032 = 0,003
𝑦 0,003
θ = 𝑇𝑎𝑛−1 = 𝑇𝑎𝑛−1 ( ) = 90º
𝑥 0
4. Calculate the current:
I = V . JωC = (12∟45°) . (0,003∟90°) = 0,036∟135°A
5. Change to time form:
I(t) = 0,036 Cos (60t + 135°)
Problem 2:
If the source voltage Vs = 20 Sin (10t + 30º) V, is applied to a resistor with a
resistance of 4 Ohms and is placed in series with the inductor of 0.2 H. Determine
the voltage v(t) and current i(t) in the time domain, and prove that:
a. 8,944 sin (10t + 93,43) V
b. 4,472 Sin (10t + 3,43) A
Solution 2:
1. Determine the parameter:
V = 20∟30º ; ω = 10t ; Z = ?
2. Find Z value:
, Z = R + jωL = 4 + j10 . 0,2 = 4 + j2
3. Polarize the 4 + j2 value using r and θ:
r = √𝑥 2 + 𝑦 2 = √42 + 22 = √20 = 4,472
𝑦 2
θ = 𝑇𝑎𝑛−1 = 𝑇𝑎𝑛−1 ( ) = 26,57º
𝑥 4
4. Calculate the current:
𝑉𝑠 20∟30°
I= = = 4,472∟3,43°A
𝑍 4,472∟26,57°
5. Calculate the voltage:
V = I . jωL = (4,472∟3,43°) . (2∟90°) = 8,944∟93,43°V
6. Convert them into the time form:
I(t) = 4,472 Sin (10t + 3,43°)A
V(t) = 8,944 Sin (10t + 93,43°)V
Problem 3:
Prove that the capacitor voltage 𝑉0 (t) in the circuit below is 𝑉0 = 14.14 Cos (10t
- 35°)V, V= 20 Cos (10t + 100°).
Solution 3:
1. Determine the parameter:
1
V = 20 Cos (10t + 100°); ω = 10(t); C = 𝐹; V = 20∟100°;
20
2. Calculate 𝑍1 value:
1 1 1
𝑍1 = = 1 = 1 = -j2 Ohm
𝑗𝜔𝐿 𝑗10 . 𝑗
2 2
3. Calculate 𝑍2 value and find 𝑍3 :
𝑍2 = jωL = j10 . 0,5 = j5 Ohm- and 𝑍3 = 10 Ohm
4. Calculate the total of impedance:
𝑍𝑇 = (𝑍2 ||𝑍3 ) + 𝑍1 = (j5||10) + (-j2) = 2 + j2
5. Polarize the total of impedance using r and θ:
