Question

What is the power dissipated in an ac circuit in which voltage and current are given by
$V=230\sin \left(\omega t+{\displaystyle \frac{\pi }{2}}\right)$ and $I=10\sin \omega t$ .

Answer 1

Hint: Power dissipation is the process by which an electronics device produces heat. Here we need to calculate the power dissipated in a circuit where voltage and current is known. Apply ac power dissipated formula we can calculate the power i.e. $P=VI\cos \varphi$ .

Complete step by step solution:
According to the problem,
Ac voltage across the circuit is given by
$V=V_o\sin \left(\omega t+\varphi \right)$
As per the question
$V=230\sin \left(\omega t+{\displaystyle \frac{\pi }{2}}\right)\cdot \cdot \cdot \cdot \left(1\right)$
Where $V_o=230V$
And $\varphi ={\displaystyle \frac{\pi }{2}}$
Now Ac current across the circuit is given by
$I=I_o\sin \left(\omega t+\varphi \right)$
As per the question
$I=10\sin \left(\omega t\right)\cdot \cdot \cdot \cdot \left(2\right)$
Where $I_o=10A$
And $\varphi =0^{\circ }$
We know that,
Power dissipated in an ac circuit
$P=V_o{I}_o\cos \varphi \cdot \cdot \cdot \cdot \left(3\right)$
Where, $\cos \varphi$ is to power factor and $\varphi$ be the phase difference
From equation $\left(1\right)and\left(2\right)$, we get
$\varphi ={\displaystyle \frac{\pi }{2}}$
Where $\varphi$ is the phase difference between V and I
Now putting the value $V_{o}and{I}_o$ respectively in equation $\left(3\right)$,we get
$P=230\times 10\times \cos {\displaystyle \frac{\pi }{2}}$
$\Rightarrow P=0W$
The SI unit of power is watt.
Therefore, the power dissipated in an ac circuit will be $zeroW$.

Additional Information:
$V$=Instantaneous value of the voltage
$I$=Instantaneous value of the current
$V_o$= Amplitude of voltage
$I_o$= Amplitude of current

Note: Generally there will be mistakes while putting the value of V and I in the power dissipated formula. Many of us put the instantaneous value of voltage and current instead of putting the amplitude of voltage and current respectively.