Phasor relation between different voltages and currents:
In the capacitive circuit of Figure, find
1. Impedance,
2. Resultant current,
3. Power factor,
4. Power absorbed by the circuit, and
5. Phasor relation between different voltages and currents.
![1317_Phasor relation between different voltages and currents.png](https://www.expertsmind.com/CMSImages/1317_Phasor relation between different voltages and currents.png)
Figure
Solution
(a) The capacitive reactance is given by
X C = 1 / ωC = 1/2π fC
= 1 / (2π× 50 × 1 × 10- 6)
= 3182.68 Ω
So the impedance, Z = R -j X C
= 120 - j 3182.68 Ω
In polar form, Z = 3184.94 ∠ - 87.84o Ω
(b) Resultant current
i = v/ Z = 100 ∠ 0o / 3184.94 ∠- 87.84o
= 0.03139 ∠ 87.84o Amp (leading)
(c) Power factor, cos φ = cos 87.84o
= 0.0376 (lead)
(d) Power is absorbed only by resistor and that is also known as the active power in the circuit
P = I 2 R
= (0.03139)+ × 120
= 0.1182 Watts
(e) Voltage drop across resistor :
VR = iR
= 0.03139 ∠ 87.84o × 120
= 3.7668 ∠ 87.84o Volt (in phase with current i)
Voltage drop across capacitor
Vc = i (- j X c )
= 0.03139 ∠ 87.84 × 3182.68 ∠ - 90o
= 99.9 ∠ - 2.16o (lagging)
The phasor diagram is shown in Figure 4.25 and applied Voltage of 100 ∠ 0o is taken as reference.
![2233_Phasor relation between different voltages and currents1.png](https://www.expertsmind.com/CMSImages/2233_Phasor%20relation%20between%20different%20voltages%20and%20currents1.png)
Figure: Phasor Diagram