Question

The current through an inductor of $1H$ is given by $i=3t\sin \left(t\right)$. The voltage across the inductor of $1H$ is

• A. $3\left(\sin t+3\cos t\right)$
• B. $3\left(\sin t+t.\cos t\right)$
• C. $4\left(\sin t+5\cos t\right)$
• D. $8\left(3\sin t+5\cos t\right)$

Answer 1

The correct option is B

$3\left(\sin t+t.\cos t\right)$

Step 1. Given data:

Inductance = $1H$

Current is given by $i=3t\sin \left(t\right)$.

Step 2. Formula used:

For a purely inductive circuit, the induced emf/voltage across the inductor when a current is passed would be

$\left|e\right|=\left|L.\frac{∆i}{∆t}\right|=\left|L.\frac{di}{dt}\right|$

Where $e$= current, $L$= inductance,

Step 3. Calculations:

$\frac{di}{dt}=3\left[\sin t+t.\cos t\right]$

$$\begin{gathered} e=1H\times 3[\sin t+t.\cos t] \\ \Rightarrow e=3[\sin t+t.\cos t] \end{gathered}$$

Thus, the correct option is option B.