The instantaneous values of alternating current and voltages in a circuit are given as $i = \frac{1}{\sqrt{2}}

Question

The instantaneous values of alternating current and voltages in a circuit are given as $i = \frac{1}{\sqrt{2}} \sin(100\pi t)$ ampere and $e = \frac{1}{\sqrt{2}} \sin(100\pi t + \pi/3)$ volt. The average power in Watts consumed in the circuit is:

Accepted Answer

The average power ($P$) consumed in an AC circuit is determined by the RMS values of voltage and current and the cosine of the phase difference (power factor). The formula is $P = V_{rms} I_{rms} \cos \phi$ .

1.  **Identify Peak Values:** From the given equations $i = I_m \sin(\omega t)$ and $e = V_m \sin(\omega t + \phi)$, we have peak current $I_m = 1/\sqrt{2}$ A and peak voltage $V_m = 1/\sqrt{2}$ V.
2.  **Calculate RMS Values:** 
    *   $I_{rms} = \frac{I_m}{\sqrt{2}} = \frac{1/\sqrt{2}}{\sqrt{2}} = \frac{1}{2}$ A.
    *   $V_{rms} = \frac{V_m}{\sqrt{2}} = \frac{1/\sqrt{2}}{\sqrt{2}} = \frac{1}{2}$ V.
3.  **Identify Phase Difference:** The phase difference $\phi$ is given as $\pi/3$ radians (or $60^\circ$).
4.  **Calculate Power:** 
    *   $P = (\frac{1}{2}) (\frac{1}{2}) \cos(\frac{\pi}{3})$
    *   $P = \frac{1}{4} 	imes \frac{1}{2} = \frac{1}{8}$ W.

Step-by-Step Solution

Practice All PHYSICS Questions