Question

An inductor of inductance 5.0 H, having a negligible resistance, is connected in series with a $100\Omega$ resistor and a battery of emf 2.0 V. Find the potential difference across the resistor 20 ms after the circuit is switched on.

Answer 1

Here $L=5.0H,$

$R=100\Omega ,emf=2.0V$

$t=20ms=20\times {10}^{-3}x$

$=2\times {10}^{-2}s$

$i_0=\frac{2}{100}$

$\tau =\frac{L}{R}=\frac{5}{100}$

Now $i=i_0(1-e^{-t/\tau })$

$i=\frac{2}{100}(1-e^{\frac{-2\times {10}^{-2}\times 100}{5}})$

$i=\frac{2}{100}(1-e^{-2/5})$

$=\frac{2}{100}(-0.670)$

$=0.00659=0.0066$

$V=iR=0.0066\times 100$

$=0.66V.$