Question

The magnetic potential energy stored in a certain inductor is $25\ \text{mJ}$, when the current in the inductor is $50\ \text{mA}$. This inductor is of inductance

• A. $2.00\ \text{H}$
• B. $0.20\ \text{H}$
• C. $200\ \text{H}$
• D. $20\ \text{H}$

Hint:

Always ensure units are converted to standard SI units (Joules for energy, Amperes for current) before substituting into the formula to avoid power-of-ten errors.

Answer 1

The Correct Option is D

Step 1: Recall the energy formula.
The energy stored in an inductor is $U = \tfrac12 L I^2$. We rearrange it to find $L = \tfrac{2U}{I^2}$.

Step 2: Switch to SI units.
$U = 25\ \text{mJ} = 25\times10^{-3}\ \text{J}$ and $I = 50\ \text{mA} = 5\times10^{-2}\ \text{A}$.

Step 3: Substitute.
\[ L = \frac{2(25\times10^{-3})}{(5\times10^{-2})^2} = \frac{50\times10^{-3}}{25\times10^{-4}}. \]

Step 4: Simplify.
$\tfrac{50}{25}\times\tfrac{10^{-3}}{10^{-4}} = 2\times10 = 20$. \[ \boxed{20\ \text{H}} \]