Q 12-06-082JEE MainJEE Main 2023 (13 Apr, Shift 1)Medium
In the given figure, an inductor and resistor are connected in series with a battery of emf $E$ volt. $\dfrac{E^a}{2b}\ \text{J s}^{-1}$ represents the maximum rate at which the energy is stored in the magnetic field (inductor). The numerical value of $\dfrac ba$ will be ______.
Numerical value type. Enter your answer.
Answer: 25
Rate of energy storage $P=Li\dfrac{di}{dt}=i(E-iR)=Ei-i^2R$.
It is maximum at $i=\dfrac E{2R}$: $P_{max}=\dfrac{E^2}{4R}=\dfrac{E^2}{100}=\dfrac{E^2}{2\times50}$.
So $a=2$, $b=50$ and $\dfrac ba=25$.
Solution by Sreeraj P, M.Sc Physics