Question

What is the power dissipated in AC circuit in which voltage and current given by
$v = 230\sin (\omega t + \dfrac{\pi }{2})$ and $I = 20\sin \omega t$ ?

Answer 1

Learn about the power dissipated through an AC circuit. The power dissipated from a circuit is given by the product of the voltage and current through the circuit. For an AC circuit the power dissipated is the average taken over a period of time

Formula used:
The average power dissipated from an AC circuit is given by,
$P = \dfrac{1}{2}{V_0}{I_0}\cos \varphi$
where, ${V_0}$ is the amplitude of the voltage applied ${I_0}$ is the amplitude of the current through the circuit $\varphi$ is the phase difference between the current and the voltage.

Complete step by step answer:
We have given here the voltage of the circuit is $v = 230\sin (\omega t + \dfrac{\pi }{2})$ where, amplitude of the voltage is ${V_0} = 230V$ , $\omega$ is the frequency of the source applied $\dfrac{\pi }{2}$ is the initial phase of the voltage. The current through the circuit is given by, $I = 20\sin \omega t$ where, ${I_0} = 20A$ is the amplitude of the current through the circuit$\omega$ is the frequency of the source applied. So, the phase difference between the current and voltage is $\varphi = \dfrac{\pi }{2}$.

Now, we know that the average power dissipated from an AC circuit is given by,
$P = \dfrac{1}{2}{V_0}{I_0}\cos \varphi$
where, ${V_0}$ is the amplitude of the voltage applied ${I_0}$ is the amplitude of the current through the circuit $\varphi$ is the phase difference between the current and the voltage.

So, here we have, amplitude of the voltage is ${V_0} = 230V$ , amplitude of the current through the circuit ${I_0} = 20A$and phase difference between the current and the voltage is $\varphi = \dfrac{\pi }{2}$. Hence putting the values we have,
$P = \dfrac{1}{2}200 \times 20 \times \cos \dfrac{\pi }{2}$
$\Rightarrow P = \dfrac{1}{2}200 \times 20 \times 0$
$\therefore P = 0$

Hence, the average power dissipated through the circuit is $0\,watt$.

Note: In the given circuit the maxima of voltage meets the minima of the current so the average value of the power becomes zero for a full circle. The average power dissipated through the circuit is zero does not mean that no energy is being exerted by the source in the circuit.