Question

The current in a coil of self-inductance $2.0\text{H}$ is increasing according to equation $I=2\sin t^2\text{A}$. Find the amount of energy spent during the period when the current changes from $0$ to $2\text{A}$.

• A. $2\text{J}$
• B. $3\text{J}$
• C. $4\text{J}$
• D. $\text{None of these}$

Answer 1

The correct option is C $4\text{J}$

For current changing from $0\to i$ the energy stored in inductor is given by:
$U={\int }_0^{i}Lidi...\left(i\right)$
given, current varries from $0$ to $2\text{A}$,
$\Rightarrow U=\frac{1}{2}L{\left[i^2\right]}_0^2=\frac{1}{2}\times 2\times 2^2=4\text{J}$

$\therefore 4\text{J}$ is the amount of energy spent during this time interval as pure inductor dose not dissipates energy.