# Q 7.15 (b)  A $100\mu F$ capacitor in series with a $40\Omega$ resistance is connected to a $110\; V$,  $60\: Hz$  supply. What is the time lag between the current maximum and the voltage maximum?

In the case of a capacitor, we have

$tan\phi=\frac{\frac{1}{wC}}{R}=\frac{1}{wCR}$

So,

$tan\phi=\frac{1}{wCR}=\frac{1}{2\pi 60 *100*10^{-6}*40}=0.6635$

$\phi=33.56^0$

So the time lag between max voltage and the max current is :

$t=\frac{\phi }{w}=\frac{33.56\pi}{180*2\pi*60}=1.55ms$

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