Question

An inductor $L$ and a resistor $R$ are connected in series with a direct current source of emf $E$. The maximum rate at which energy is stored in the magnetic field is

• A. $\frac{E^2}{4R}$
• B. $\frac{E^2}{R}$
• C. $\frac{{4E}^2}{R}$
• D. $\frac{{2E}^2}{R}$

Answer 1

The correct option is A $\frac{E^2}{4R}$

Rate of change of energy stored in Magnetic field is given by, $P=Li\frac{di}{dt}$

and in Inductive circuit rate of change of current is maximum at time instant $t=0$,

i.e. Current in inductor is given by, $i=I_o(1-e^{\frac{-t}{\tau }})$

where, $\tau =\frac{L}{R}$

So, $\frac{di}{dt}=\frac{I_o}{\tau }$

Hence, maximum rate of energy stored is, $P_{max}|t=0=L{I}_o\frac{I_o\times R}{L}=I_o^{2}R=\frac{E^2}{R}$