Question

Initially there is no current in the circuit, at $t=0sec$. The growth rate of current at $t=0$ is r. After a long time when current becomes constant and is equal to $i$.

• A. $r=0andi=\frac{\epsilon }{R}$
• B. $r=\frac{\epsilon }{L}andi=\frac{\epsilon }{R}$
• C. $r=\frac{\epsilon }{L}andi=0$
• D. $r=\frac{L}{\epsilon }andi=\frac{\epsilon }{R}$

Answer 1

The correct option is B $r=\frac{\epsilon }{L}andi=\frac{\epsilon }{R}$

At $t=0$, $i=0$, so the voltage across the inductor is $\epsilon$.
$L\times \frac{di}{dt}=\epsilon \Rightarrow \frac{di}{dt}=\frac{\epsilon }{L}$
$r=\frac{\epsilon }{L}$
At $t\to \infty$, voltage across the inductor is zero.
$\therefore \epsilon =iR\Rightarrow i=\frac{\epsilon }{R}$