Question

A solenoid has self inductance of $5\text{mH}$ and the current through it is given by $i=5t^2$ where $t$ is time in second. The induced emf at $t=1\text{s}$ is -

• A. $50\text{mV}$
• B. $40\text{mV}$
• C. $30\text{mV}$
• D. $20\text{mV}$

Answer 1

The correct option is A $50\text{mV}$

Given :

Self inductance, $L=5\text{mH}=5\times {10}^{-3}\text{H}$

Current, $i=5t^2$

$\Rightarrow \frac{di}{dt}=10t$

At $t=1\text{s},\frac{di}{dt}=10\text{A/s}$

So, induced emf,

$E=-L\frac{di}{dt}=-5\times {10}^{-3}\times 10=-5\times {10}^{-2}\text{V}=-50\text{mV}$

$\Rightarrow |E|=50\text{mV}$