Question

A 100 $\mu$F capacitor in series with a 40 $\Omega$ resistance is connected to a 110 V, 60 Hz supply.

(a) What is the maximum current in the circuit?

(b) What is the time lag between the current maximum and the voltage maximum?

Answer 1

(a)

$\omega =2\pi f=120\pi rad/s$

$Z^2=R^2+\frac{1}{{\omega }^2{C}^2}$

$⟹Z\approx 48\Omega$

$V_0=V\sqrt{2}=110\sqrt{2}$

$I_o=V_o/Z=3.24A$

(b)

$tan\varphi =\frac{1/\omega C}{R}=0.6635$

$\varphi =33.56\pi /180rad$

Time lag is $\varphi /\omega =1.55ms$