Alternating Current

# Wattless Current

## Wattless Current

The current which consumes no power is called wattless current or idle current. In a circuit containing pure inductor or capacitor, the phase angle between voltage and capacitor is $\frac{π}{2}$. [AC Through Circuit Elements] Hence, power consumed in such circuit is given by $P_{\text{av}}=E_{\text{rms}}I_{\text{rms}}\cos\frac{π}{2}=0$

Hence, the average power in a purely inductive or capacitive circuit is zero even though a current is passed through it. This current is called wattless current.

## Wattful Current

At resonance, the impedance of the LCR series circuit becomes minimum and the circuit allows maximum current. Resonance occurs when inductive reactance $(X_L)$ becomes equal to capacitive reactance $(X_C)$. The circuit becomes purely resistive and hence the voltage $(E)$ and the current $(I)$ are in same phase i.e. $\theta=0°$. [From: AC Through a Resistor (AC Through Circuit Elements)]

$\therefore\cos\theta=\cos 0°=1$ $\therefore P_{text{av}}=E_{\text{rms}}I_{\text{rms}}$ Hence, maximum power is dissipated in a circuit at resonance. This current at resonance is called wattful current.

Hence, the current through the resistance $R$ which consumes power for its maintenance is called wattful current.

## Choke Coil

In a dc circuit, the current can be reduced by using suitable resistance. But resistance produces heat. So, electrical energy is wasted in the form of heat. [Joule’s Laws of Heating (DC Circuit)]

But in an ac circuit, the current can be reduced without any loss of electrical energy. This can be done by using a suitable inductor. In an inductor, the phase angle between voltage and current is $\frac{π}{2}$. [From: AC Through an Inductor (AC Through Circuit Elements)] Hence, power consumed is zero i.e. $P=E_{\text{rms}}I_{\text{rms}}\cos\frac{π}{2}=0$ Such an inductor used to control current in an ac circuit is known as choke or choke coil.

However, a real inductor also possesses some small resistance, therefore it may be treated as a circuit having inductance and resistance connected in series (LR circuit).

A choke coil is simply a coil of large inductance and very small resistance. Due to the presence of resistance, it will consume a small amount of power given by $P=E_{\text{rms}}I_{\text{rms}}\cos\theta=E_{\text{rms}}I_{\text{rms}}\frac{R}{\sqrt{R^2+\omega^2L^2}}$ Here, $\cos\theta=E_{\text{rms}}I_{\text{rms}}\frac{R}{\sqrt{R^2+\omega^2L^2}}$ is known as the power factor of LR circuit.

In practice, a low frequency choke coil is made of insulated copper wire on a soft iron core, while a high frequency choke coil has air as core.