Question

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

• A. $0$
• B. $2\text{J}$
• C. $4\text{J}$
• D. $10\text{J}$

Answer 1

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

Energy stored in an inductor is, $U=\frac{1}{2}L{i}^2$

The initial energy stored in the inductor is,

$U_i=\frac{1}{2}\times 2\times 0^2=0\text{J}[\because i=0\text{A}]$

The final energy stored in the inductor when current is,

$U_f=\frac{1}{2}L{i}^2=\frac{1}{2}\times 2\times (2{)}^2=4\text{J}[\because i=2\text{A}]$

$\therefore$ Amount of energy spent during this period is,

Energy spent, $\Delta U=U_f-U_i=4-0=4\text{J}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(\text{C}\right)$ is the correct answer.

Why this question ? The expression of current is given in the question only to confuse you. Energy spent depends only on the initial and final value of the current.

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