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).

Circuit Diagram of Choke Coil (Wattless Current)

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.

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