Q 12-07-063JEE MainJEE Main 2024 (9 Apr, Shift 1)Easy
When a coil is connected across a $20\ \text{V}$ dc supply, it draws a current of $5\ \text{A}$. When it is connected across a $20\ \text{V}$, $50\ \text{Hz}$ ac supply, it draws a current of $4\ \text{A}$. The self inductance of the coil is ______ mH. (Take $\pi = 3$)
Numerical value type. Enter your answer.
Answer: 10
DC: $R = \dfrac{20}{5} = 4\ \Omega$. AC: $Z = \dfrac{20}{4} = 5\ \Omega$, so $X_L = \sqrt{5^2 - 4^2} = 3\ \Omega$.
$$L = \frac{X_L}{2\pi f} = \frac{3}{2\times3\times50} = 0.01\ \text{H} = 10\ \text{mH}$$
Solution by Sreeraj P, M.Sc Physics