Question

A coil of inductance $5H$ is joined to a cell of emf $6V$ through a resistance of $10\Omega$ at $t=0$ . The emf across the coil at time $t=ln\left(\sqrt{2}\right)$ sec is

• A. 3 V
• B. 1.5 V
• C. 0.75 V
• D. 4.5 V

Answer 1

Answer: (A)

$i=\frac{ϵ}{R}\left(1-e^{-\frac{tR}{L}}\right)$
$\therefore$ Emf across R is ${\left(ϵ\right)}_R=ϵ\left(1-e^{-\frac{tR}{L}}\right)$
$\Rightarrow {\left(ϵ\right)}_R=6V\left(1-e^{-ln\sqrt{2}.2}\right)$
$\Rightarrow {\left(ϵ\right)}_R=6V\left(1-\frac{1}{2}\right)=3V$
$\therefore$ Voltage across coil ${ϵ}_c=ϵ-{ϵ}_R=3$ volt