Phasor relation between different voltages and currents, Electrical Engineering

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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

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

Figure: Phasor Diagram


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