Question

A resistance of $40\Omega$ is connected to a source of alternating current rated $220V,50Hz$. Find the time taken by the current to change from its maximum value to rms value :

• A. $2.5ms$
• B. $1.25ms$
• C. $2.5s$
• D. $0.25s$

Answer 1

Answer: (A)

Considering sinusoidal $AC$.
Phase at maximum value $=\frac{\pi }{2}$
Phase at rms value $=\frac{3\pi }{4}$
Thus phase change $=\frac{3\pi }{4}-\frac{\pi }{2}=\frac{\pi }{4}$
Now $\omega =2\pi f$
$=2\pi \times 50$
$=100\pi$
time taken $t=\frac{\theta }{\omega }=\frac{\pi /4}{100\pi }=\frac{1}{400}s$
$t=2.5\times 10^{-3}=2.5ms$