Question 9: Electromagnetic Induction

Question

A current of 2 A is passed through the primary coil. The total flux linked with the secondary coil, which is closely wound over the primary is $2000 	imes 10^{-6}$ weber. What is the induced emf in the secondary if the current through the primary increases at a rate of $0.2 \mathrm{As}^{-1}$ ?

Accepted Answer

First, recall that the induced emf in the secondary is
$$\mathcal{E} \;=\; -\frac{d\Lambda}{dt}$$
where $\Lambda$ is the total flux linkage. If the flux linkage is proportional to the primary current $I$, then
$$\Lambda = k\,I\quad\Longrightarrow\quad \frac{d\Lambda}{dt}=k\,\frac{dI}{dt}$$
and since $k=\Lambda/I$, we get
$$\bigl|\mathcal{E}\bigr| \;=\;\frac{\Lambda}{I}\,\frac{dI}{dt}\,. $$
Given:
Ã¢ÂÂ¢ $\Lambda=2000	imes10^{-6}$ Wb
Ã¢ÂÂ¢ $I=2$ A
Ã¢ÂÂ¢ $\dfrac{dI}{dt}=0.2$ A/s
Hence
$$\bigl|\mathcal{E}\bigr| =\frac{2000	imes10^{-6}}{2}	imes0.2 =1000	imes10^{-6}	imes0.2 =200	imes10^{-6}\;{m V} =2	imes10^{-4}\;{m V}\,. $$
Answer: Option A) $2	imes10^{-4}$ V.

Answer

$2 	imes 10^{-4} V$

Answer

$4 	imes 10^{-4} V$

Answer

$1 	imes 10^{-4} V$

Answer

$8 	imes 10^{-4} V$

Electromagnetic Induction

A current of 2 A is passed through the primary coil. The total flux linked with the secondary coil, which is closely wound over the primary is 2000 \times 10^{-6} weber. What is the induced emf in the secondary if the current through the primary increases at a rate of 0.2 \mathrm{As}^{-1} ?

Choose the correct answer: