Question

A $100\,\mu F$ capacitor in series with a $40\,\Omega$ resistor is connected to a $100\,V$, $60\,Hz$ supply, the time lag between the current maximum and the voltage maximum is

• A. $15.5\,ms$
• B. $155\,ms$
• C. $1.55\,ms$
• D. $15\,ms$

Answer 1

Answer: (C)

In series $RC$ circuit voltage lags behind the current by phase angle $\phi$.
Then, $tan\,\phi=\frac{X_{C}}{R}=\frac{1 / \omega C}{R}=\frac{1}{\omega\,CR}=\frac{1}{2\pi\upsilon CR}$
$tan\,\phi -\frac{1}{2\pi\times60\times10^{-4}\times40}$
$tan\,\phi =\left(0.6634\right);\,\phi =tan^{-1}\left(0.6634\right)$
$=33.56^{\circ}=33.56\times\frac{\pi}{180}rad$
$\therefore $ Time lag, $\Delta t=\frac{\phi}{\omega}=\frac{180}{120\,\pi}=1.55\times10^{-3}\,s\,\left[\because \omega=2\pi\upsilon=120\pi\right]$
$=1.55\,ms$