Question

A 10 V battery connected to 5 $\Omega$ resistance coil having inductance 10 H through a switch drives a constant current in the circuit. The switch is suddenly opened and the time taken to open it is 2 ms. The average emf induced across the coil is

• A. $4\times {10}^4$
• B. $2\times {10}^4$
• C. $2\times {10}^2$
• D. $1\times {10}^4$

Answer 1

The correct option is D $1\times {10}^4$

Here,

current $I=\frac{V}{R}=\frac{10}{5}=2A$

Final current, when the switch is opened is zero.
$\therefore \frac{dI}{dt}=\frac{0-2}{2\times {10}^{3-}}=1\times {10}^{-3}A{s}^{-1}$

$As\epsilon =-L\frac{dI}{dt}=-10(-1\times {10}^3)={10}^{4}V$