Question

Two coils have self inductance \(L_1\) and \(L_2\). The current through them is increasing at constant rate. If the power dissipated in both the coils is same, then the ratio of energy stored in the coil having inductance \(L_1\) to that in \(L_2\) is

• A. \(\frac{L_1^2}{L_2^2}\)
• B. \(\frac{L_2^2}{L_1^2}\)
• C. \(\frac{L_1}{L_2}\)
• D. \(\frac{L_2}{L_1}\)

Hint:

Power in an inductor is \(P=LI\frac{dI}{dt}\), and energy is \(U=\frac12LI^2\).

Answer 1

The Correct Option is D

Step 1: Express energy through power
$U=\tfrac12LI^2=\dfrac{(LI)^2}{2L}$, and $LI=\dfrac{P}{dI/dt}$ is the same for both coils.

Step 2: Compare
So $U\propto\dfrac1L$ and $\dfrac{U_1}{U_2}=\dfrac{L_2}{L_1}$, option (D).

Final Answer:
$U_1/U_2=L_2/L_1$, option (D). \[ \boxed{\dfrac{L_2}{L_1}} \]