Why Power in Pure Inductive and Pure Capacitive Circuit is Zero?

Power In a Pure Inductive Circuit

The active power drawn by a pure inductive and a pure capacitive circuit is zero.In a pure inductive circuit the current lags the voltage by 90° because the inductive load always opposes the rate of change of current.

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pure inductive circuit diagram

The back EMF or counter EMF generated in the inductive load due to rate of change of the current.The back EMF generated in the inductive circuit is given by.

back emf in pure inductive circuit- formula

 

 

The minus sign indicates that the voltage induced in the inductive circuit opposes the applied voltage. Because of this opposition, the current through the inductive load lags the voltage. If the load is purely inductive the phase angle between the applied voltage and the current is 90°. The waveform of current and voltage in the purely inductive circuit is as shown below.

voltage & current in pure inductive circuit- waveform

The voltage and current in a purely inductive circuit do not rising or falling together.There is always phase shift of 90° between voltage and current.The power factor of the purely inductive circuit is ;

voltage & current phasor of pure inductive circuit

The power in a AC circuit is given by;

P = VICosΦ    ———–(1)

The power factor of the purely inductive circuit is zero(lagging).

CosΦ = 0    ———–(2)

The power in a purely inductive circuit is given by,

P = VICosΦ 

P = VI x 0

P = 0

Thus, the pure inductive circuit consumes zero active power and it consumes reactive power only from the supply source.

Power in a Pure Capacitive Circuit

In a pure capacitive circuit the current leads the voltage by 90° because the capacitive load always opposes the rate of change of voltage.The Pure capacitive circuit is as given below.

pure capacitive circuit voltage & current relationship


The current through the capacitor leads the applied voltage by 90°.

Image result for pure capacitive circuit- phasor diagram

The Power factor of a pure capacitive load is zero(leading).

power factor in ac circuit

The power in a AC circuit is given by;

P = VICosΦ    ———–(3)

The power factor of the purely capacitive circuit is zero(leading).

CosΦ = 0    ———–(4)

The power in a purely inductive circuit is given by,

P = VICosΦ
P = VI x 0
P = 0

Thus, a pure capacitive circuit consumes zero active power. The pure capacitive circuit consumes reactive power from the supply source.

Mathematical Proof:

The active power drawn by a pure capacitive load can be mathematically proved to be zero.

Power in Pure Inductive and Pure Capacitive Circuit is Zero- Mathematical Proof

 

 

 

 

 

 

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