Question

An $\text{LR}$ series circuit has $L=1\text{H}\text{and}R=1\Omega$. If it is connected across an emf of $2\text{V}$ then

• A. The maximum rate at which energy is stored in the magnetic field is $1\text{W}$
• B. The maximum rate at which energy is stored in the magnetic field is $2\text{W}$
• C. The current at that instant is $1\text{A}$
• D. The current at that instant is $2\text{A}$

Answer 1

Answer: (A), (C)

The current at that instant is $1\text{A}$


$L=1\text{H}$ and $R=1\Omega$

Assume that at a instant current in the circuit is $I$.

From conservation of energy:

rate of energy stored (in inductor) $r=EI-I^{2}R$

Differentiating with respect ot $I$ on both sides,

$\frac{dr}{dI}=E-2IR=0$

$I=\frac{E}{2R}$ , for $r_{max}$

$r_{max}=E\times \frac{E}{2R}-{\left(\frac{E}{2R}\right)}^{2}R=\frac{E^2}{4R}=\frac{(2{)}^2}{4\times 1}=1\text{A}$

Hence, options (a) and (c) are the correct answers.