Question

Two coils have seld inductance $12$mH and $3$mH respectively. The currents in the two coils are increased at the same rate. At a certain instant of time both the coils are given the same power. If $I_1$ and $I_2$ are the currents in the two coils, then $\frac{I_1}{I_2}$ is?

• A. $1:2$
• B. $2:1$
• C. $4:1$
• D. $1:4$

Answer 1

The correct option is D $1:4$

The induced emf is given by
$e=-L\frac{di}{dt}$
So $|e|=L\frac{di}{dt}$
$\Rightarrow L=\frac{e}{\frac{di}{dt}}$
Also power is the product of voltage and current.
So, $P=e\times I$
$\Rightarrow e=\frac{P}{I}$
$\therefore L=\frac{P/I}{\frac{di}{dt}}=\frac{P}{i\left(\frac{di}{dt}\right)}$
Given, P and $\frac{di}{dt}$ are constants.
$\therefore L\propto \frac{1}{i}$
$\therefore \frac{I_1}{I_2}=\frac{L_2}{L_1}=\frac{3}{12}=\frac{1}{4}$.