Question

For a domestic AC supply of 220 V at 50 cycles per sec, the potential difference between the terminals of a two-pin electric outlet in a room is given by

• A. \( V(t)=220\sqrt{2}\cos(100\pi t) \)
• B. \( V(t)=220\sin(50t) \)
• C. \( V(t)=220\cos(100\pi t) \)
• D. \( V(t)=220\sqrt{2}\cos(50t) \)

Hint:

AC voltage: \begin{itemize} \item \( V_0=\sqrt{2}V_{\text{rms}} \) \item \( \omega=2\pi f \) \end{itemize}

Answer 1

The Correct Option is A

Concept: AC voltage form: \[ V(t)=V_0\cos(\omega t) \] where \( V_0=\sqrt{2}V_{\text{rms}} \) and \( \omega=2\pi f \). Step 1: {\color{red}Given data.} \[ V_{\text{rms}}=220 \text{ V}, \quad f=50\text{ Hz} \] Step 2: {\color{red}Find peak voltage.} \[ V_0=220\sqrt{2} \] Step 3: {\color{red}Angular frequency.} \[ \omega=2\pi f=100\pi \] Step 4: {\color{red}Write expression.} \[ V(t)=220\sqrt{2}\cos(100\pi t) \]