Question

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

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

Answer 1

Answer: (C)

In series $RC$ circuit voltage lags behind the current by phase angle $\varphi$.
Then, $tan\varphi =\frac{X_C}{R}=\frac{1/\omega C}{R}=\frac{1}{\omega CR}=\frac{1}{2\pi \upsilon CR}$
$tan\varphi -\frac{1}{2\pi \times 60\times 10^{-4}\times 40}$
$tan\varphi =\left(0.6634\right);\varphi =ta{n}^{-1}\left(0.6634\right)$
$=33.56^{\circ }=33.56\times \frac{\pi }{180}rad$
$\therefore$ Time lag, $\Delta t=\frac{\varphi }{\omega }=\frac{180}{120\pi }=1.55\times 10^{-3}s\left[\because \omega =2\pi \upsilon =120\pi \right]$
$=1.55ms$