Q11Basic Electrical Engineering

The standard mathematical equation for an alternating voltage is given by $v(t)=V_m\sin (\omega t)$, where $V_m$ is the peak maximum amplitude and $\omega$ is the angular frequency. By comparing the given equation $V=230\sin (314t)$ with the standard form, we can systematically extract the required parameters.

(i) Maximum Value ($V_m$): Directly comparing the equations, the amplitude coefficient is 230. $V_m=230\text{ Volts}$.

(ii) Frequency ($f$): The angular frequency $\omega$ is given as 314 rad/sec. Since $\omega =2\pi f$: $2\pi f=314⟹f=\frac{314}{2\times 3.14159}\approx 50\text{ Hz}$.

(iii) Average Value ($V_{avg}$): For a full pure sinusoidal wave, the average value over a half cycle is defined as $0.637$ times the maximum value. $V_{avg}=\frac{2V_m}{\pi }=\frac{2\times 230}{\pi }=\frac{460}{3.14159}\approx 146.42\text{ Volts}$.

(iv) RMS Value ($V_{rms}$): The Root Mean Square (RMS) value for a sinusoidal wave is defined as the maximum value divided by $\sqrt{2}$. $V_{rms}=\frac{V_m}{\sqrt{2}}=\frac{230}{1.414}\approx 162.63\text{ Volts}$.