Question

A coil of inductance 0.50 H and resistance $100\Omega$ is connected to a 240 V, 50 Hz ac supply.

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

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

Answer 1

(a)

Peak velocity $V_0=\sqrt{2}V=339.41$

$\omega =2\pi f=100\pi rad/s$

$I_o=\frac{V_o}{\sqrt{R^2+{\omega }^2{L}^2}}=1.82A$

(b)

The voltage is given as $V=V_{o}cos\omega t$

The current is given as $I=I_{o}cos(\omega t-\varphi )$

$\varphi$ is the phase angle between the voltage and current.

The time lag is given as $\varphi /\omega$.

Now phase angle is given as $tan\varphi =\omega L/R=2\pi \times 50\times 0.5/100=1.57$.

So $\varphi =ta{n}^{-1}1.57={57.5}^o=57.5\pi /180radians$

time lag is $t=\varphi /\omega =57.5\pi /180\times 2\pi \times 50=3.19\times {10}^{-3}s$