Question

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

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

Answer 1

Answer: (A)

$V\left(t\right)=220\sqrt{2}\cos \left(100\pi t\right)$

Rms value of voltage $V_{rms}=220$ volts

Peak value of voltage $V_o=\sqrt{2}{V}_{rms}$

$\therefore$ $V_o=220\sqrt{2}$volts

Frequency $\nu =50$ $Hz$

$⟹$ $w=2\pi \nu =2\pi \left(50\right)=100\pi$

Thus potential difference is given by $V=V_o\cos wt$

$\therefore$ $V=220\sqrt{2}\cos \left(100\pi t\right)$