Chapter 9, Problem 1RQ

To determine

Find the induced emf at $t=2\text{s}$.

Answer to Problem 1RQ

The induced emf at $t=2\text{s}$ is (b) –1 V.

Explanation of Solution

Calculation:

Consider the expression to find induced emf in a coil.

$V_{\text{emf}}=-N\frac{d\psi }{dt}$

Here,

$\psi$ is the flux through each turn and

N is the number of turns.

Substitute 100 for N and $\left(t^3-2t\right)\text{mWb}$ for $\psi$.

$\begin{array}{c}{V}_{\text{emf}}=-100\frac{d}{dt}\left[\left(t^3-2t\right)\text{mWb}\right]\\ =-100\left(3t^2-2\right)\text{mV}\end{array}$

Substitute 2 for t.

$\begin{array}{c}{V}_{\text{emf}}=-100\left(3{\left(2\right)}^2-2\right)\text{mV}\\ =-100\left(10\right)\text{mV}\\ =-1000\text{mV}\\ =-1\text{V}\end{array}$

Conclusion:

Therefore, the correct option is “(b) –1 V” and the remaining options are incorrect.