Question

Two coils, A and B, are lined such that emf $ϵ$ is induced in B when the current in A is changing at the rate $I$. If $i$ current is now made to flow in B, the flux linked with A will be :

• A. $\left(ϵ/I\right)i$
• B. $ϵiI$
• C. $\left(ϵI\right)i$
• D. $iI/ϵ$

Answer 1

The correct option is A $\left(ϵ/I\right)i$

Let $M=$ mutual inductance between A and B.

${ϵ}_B=M\frac{d{i}_A}{dt}$ or ${ϵ}_B=MI$ or

$M={ϵ}_B/I$

where $I=d{i}_A/dt$

${\varphi }_A=M{i}_B=\left({ϵ}_B/I\right)i_B$

$\therefore {\varphi }_A=\left(ϵ/I\right)i$ $(\because i=i_B)$