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)

$i=\frac{\epsilon }{R}\left(1 - e^{- \frac{t R}{L}}\right)$
$\therefore $ Emf across R is $\left(\epsilon \right)_{R}=\epsilon \left(1 - e^{- \frac{t R}{L}}\right)$
$\Rightarrow \left(\epsilon \right)_{R}=6 \, V\left(1 - e^{- l n \sqrt{2} \, . \, 2}\right)$
$\Rightarrow \left(\epsilon \right)_{R}=6V\left(1 - \frac{1}{2}\right)=3 \, V$
$\therefore $ Voltage across coil $\epsilon _{c}=\epsilon -\epsilon _{R}=3$ volt