Question

Using an AC voltmeter the potential difference in an electrical line in a house is read to be 224 V if the line frequency is known to be 50 Hz. The equation of the voltage is

• A. V=317 sin$\left(50\pi t\right)$
• B. V=317 sin$\left(100\pi t\right)$
• C. V=224 sin$\left(100\pi t\right)$
• D. V=224 sin$\left(200\pi t\right)$

Answer 1

Answer: (B)

V=317 sin$\left(100\pi t\right)$

$Given:$ Voltmeter$=224V$ ; frequency $=50Hz$

$Solution:$

$V=V_0\sin \left(\omega t\right)$

Vlotage in r.m.s value $V_0=\sqrt{2}\times 224V=317volt$

and $\omega t=2\pi nt=2\pi \times 50\times t=100\pi t$

Thus, the equation of line voltage is given by

$V=317\sin \left(100\pi t\right)$

$\text{So, the correct option:B}$