KCET 2025 Physics Paper

The sinusoidal voltage from an AC generator at any instant is represented by the equation$V = 311 \sin 314 t$To determine the root mean square (rms) value of the voltage, we use the formula for the rms value of a sinusoidal voltage:$V_{\text{rms}} = \frac{V_0}{\sqrt{2}} = \frac{311}{\sqrt{2}} = 220\,\mathrm{V}$ Here, $V_0 = 311\,\mathrm{V}$ is the peak voltage.To find the frequency, we use the relationship between angular frequency $(\omega)$ and frequency $(f)$ :$\omega = 2\pi f$ Given $\omega = 314$, we set:$314 = 2\pi f$Solving for $f$, we find:$f = \frac{314}{2\pi} \approx 50\,\mathrm{Hz}$Thus, the rms value of the voltage is 220 V , and the frequency is 50 Hz .