Chapter: AC Circuits· Basic Electrical & Electronics Engineering

A sinusoidal voltage of 230 V (RMS), 50 Hz is applied to a circuit. Write the equation for its instantaneous value and find the time taken, measured from the zero crossing (going positive), for the voltage to reach 200 V for the first time.

Q.6 A sinusoidal voltage of 230 V (RMS), 50 Hz is applied to a circuit. Write the equation for its instantaneous value and find the time taken, measured from the zero crossing (going positive), for the voltage to reach 200 V for the first time.

Doubtly AI Asked 27 Oct 2026 AI-generated · not yet verified Practice test mu engineering Save WhatsApp Report

1 answer

Best answer

Answer: \(v=325.27\sin(314.16\,t)\) V; it reaches 200 V after \(t\approx2.11\) ms.

\(V_m=\sqrt2\,V_{rms}=\sqrt2\times230=325.27\) V, \(\omega=2\pi f=2\pi\times50=314.16\) rad/s.

\[v=V_m\sin\omega t=325.27\sin(314.16\,t)\ \text{V}.\]

For \(v=200\) V: \(\sin(314.16\,t)=\dfrac{200}{325.27}=0.6149\Rightarrow 314.16\,t=\sin^{-1}(0.6149)=0.6622\) rad (radian mode!).

\[t=\frac{0.6622}{314.16}=2.108\times10^{-3}\text{ s}\approx2.11\text{ ms}.\]

Doubtly AI · 27 Oct 2026 AI-verified · Oct 2026 Report

Was this answer helpful?

A sinusoidal voltage of 230 V (RMS), 50 Hz is applied to a circuit. Write the equation for its instantaneous value and find the time taken, measured from the zero crossing (going positive), for the voltage to reach 200 V for the first time.

1 answer

Your answer