Question

Two coils have self-inductance $L_{1} = 4 \,mH$ and $L_{2} = 1 \,mH$ respectively. The currents in the two coils are increased at the same rate. At a certain instant of time both coils are given the same power. If $I_{1}$ and $I_{2}$ are the currents in the two coils at that instant of time respectively, then the value of $\frac{I_1}{I_2}$ is

• A. $\frac{1}{8}$
• B. $\frac{1}{4}$
• C. $\frac{1}{2}$
• D. $1$

Answer 1

Answer: (B)

$\left|\varepsilon\right|=L \frac{dI}{dt}$
$L=\frac{\left|\varepsilon\right|}{dI/ dt}=\frac{IR}{dI/ dt} $
$\frac{IP/ I^{2}}{dI/ dt}=\frac{P}{I \left(dI /dt\right)}$
As $P$ and $\left(dI /dt\right)$ are same for both the coils
$\therefore \frac{I_{1}}{I_{2}}=\frac{L_{2}}{L_{1}}=\frac{1}{4}$