In an AC circuit, the instantaneous values of emf and current are \( \varepsilon = 100\sin(314t)\,\mathrm{V} \) and \( I = \sin(314t + \pi/3)\,\mathrm{A} \). The average power consumed in the circuit is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 25 W
The average power in an ac circuit is the product of the rms voltage, the rms current and the power factor \( \cos\phi \), where \( \phi \) is the phase difference between emf and current.
\( \varepsilon_0 = 100\,\mathrm{V} \)
\( I_0 = 1\,\mathrm{A} \)
\( \phi = \pi/3 = 60^\circ \)
\( \displaystyle P = \varepsilon_{\mathrm{rms}}\,I_{\mathrm{rms}}\cos\phi = \frac{\varepsilon_0}{\sqrt{2}}\,\frac{I_0}{\sqrt{2}}\cos\phi = \frac{\varepsilon_0 I_0}{2}\cos\phi \)
\( \displaystyle P = \frac{100 \times 1}{2} \times \cos 60^\circ = 50 \times \frac{1}{2} = 25\,\mathrm{W} \)