A voltage signal is given as \( V=10\sin 4\pi t \) volts. What is the rms value of the current through a circuit of resistance \( 50\,\Omega \) connected to it?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 0.14 A
For a sinusoidal voltage \( V=V_m\sin\omega t \), the rms voltage is \( V_m/\sqrt{2} \). In a purely resistive circuit, the rms current is \( I=V/R \) with \( V \) the rms voltage. Here the peak voltage is \( V_m=10\,\mathrm{V} \).
\( \begin{aligned} V &= \frac{V_m}{\sqrt{2}} \\ &= \frac{10\,\mathrm{V}}{\sqrt{2}} \\ &\approx 7.07\,\mathrm{V} \end{aligned} \)
\( \begin{aligned} I &= \frac{V}{R} \\ &= \frac{7.07\,\mathrm{V}}{50\,\Omega} \\ &\approx 0.14\,\mathrm{A} \end{aligned} \)