A voltage \( V=10\cos(10\pi t) \) volt is applied across a resistor of \( 20\,\Omega \). The rms current through it is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 0.35\,\mathrm{A} \)
For a resistor, Ohm’s law holds at every instant, so the peak current is the peak voltage divided by R. For a sinusoidal current the rms value is \( I=i_m/\sqrt{2} \). The frequency does not affect it.
From \( V=10\cos(10\pi t) \), the peak voltage is \( v_m=10\,\mathrm{V} \).
\( \begin{aligned} i_m &= \frac{v_m}{R} \\ &= \frac{10\,\mathrm{V}}{20\,\Omega} \\ &= 0.5\,\mathrm{A} \end{aligned} \)
\( \begin{aligned} I &= \frac{i_m}{\sqrt{2}} \\ &= \frac{0.5\,\mathrm{A}}{1.414} \\ &\approx 0.35\,\mathrm{A} \end{aligned} \)