Question

Magnetic flux $\varphi$ in weber in a closed circuit of resistance $10\Omega$ varies with time $t$ (in seconds) as $\varphi =6t^2-5t+1$. The magnitude of induced current at $t=0.25\text{s}$ is

​​​​​​​$[$1 Mark$]$

• A. $0.2\text{A}$
• B. $0.6\text{A}$
• C. $1.2\text{A}$
• D. $0.8\text{A}$

Answer 1

The correct option is A $0.2\text{A}$

Induced emf

$\epsilon =-\frac{d\varphi }{dt}=-\frac{d}{dt}(6t^2-5t+1)=-12t+5$

At $t=0.25\text{sec},\epsilon =-12\left(0.25\right)+5=2\text{V}$

Induced current, $I=\frac{\epsilon }{R}=\frac{2}{10}=0.2\text{A}$