Question

An inductor coil stores $0.25\text{J}$ of energy when current $i$ is passed through it and dissipates the energy at the rate of $0.5\text{W}$. The time constant of the circuit, when this coil is connected across a battery of zero internal resistance, is :

• A. $0.01\text{s}$
• B. $0.1\text{s}$
• C. $1.0\text{s}$
• D. $0.2\text{s}$

Answer 1

The correct option is C $1.0\text{s}$

According to problem, energy stored in inductor is,

$\frac{1}{2}L{i}^2=0.25\text{J}....\left(1\right)$

Where, $L$ is the inductance of the coil.

Power dissipated by the coil,

$i^{2}R=0.5\text{W}....\left(2\right)$

Where $R$ is the resistance of the coil.

Dividing equation $\left(1\right)$ and $\left(2\right)$, we get

$\frac{L}{R}=\frac{2\times 0.25}{0.5}=1\text{s}$

$\therefore$ Time constant of the circuit is,

$\tau =\frac{L}{R}=1\text{s}$

Hence, $\left(\text{C}\right)$ is the correct answer.

Why this question ? Basic concept: Transient time of any inductive circuit is determined by the time constant of $RL$ circuit.