Question

A coil of $10$ $H$ inductance has a $5$ $\Omega$ resistance and is connected to a $5$ $V$ battery in series. The current in ampere, in the circuit $2$ seconds after the circuit is switched on is

• A. $1$ $A$
• B. $(1-\frac{1}{e})A$
• C. $(1-e)$ $A$
• D. $\frac{1}{e}$ $A$

Answer 1

The correct option is B $(1-\frac{1}{e})A$

Current in a $L-R$ circuit connected to a DC Voltage source is $i=\frac{V}{R}(1-e^{-\frac{R}{L}t})$

Here, $V$ is the voltage of the battery, $R$ is the resistance of the circuit, $L$ is the inductance of the circuit and $t$ is the time in seconds after the circuit is switched on.

Given
$t=2s,V=5V,R=5\Omega ,L=10H$

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