Question

The magnetic flux linked with a coil is changing with time t(second) according to $\varphi =6t^2-5t+1$. Where $\varphi$ is in Wb. At $t=0.5$S, the induced current in the coil is __________. The resistance of the circuit is $10\Omega$.

• A. $1$A
• B. $0.1$A
• C. $0.1$mA
• D. $10$A

Answer 1

The correct option is B $0.1$A

We know that the rate of change in flux is equal to the e.m.f produced.

$\Rightarrow$ $ϵ=\frac{\partial \varphi }{\partial t}$

$\Rightarrow$ $ϵ=\frac{\partial (6t^2-5t+1)}{\partial t}=12t-5$

at $t=0.5s$, $ϵ=12\times 0.5-5=1V$

So, Induced current = $\frac{V}{R}=\frac{1}{10}A=0.1A$

Therefore B is correct option.