Question

A coil of inductance 5H is joined to a cell of emf 6V through a resistance $10\Omega$ at time t = 0.The EMF across the coil at time t = In $\sqrt{2}s$ is:

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

Answer 1

The correct option is A 3 V

Given,

Resistance, $R=10\Omega$

Inductance, $L=5H$

Emf of cell $V=6V$

$i_0=\frac{V}{R}=\frac{6}{10}=0.6$
formula for current in inductor.

$i=i_0(1-e^{\frac{-Rt}{L}})$ at time $t=\ell n\sqrt{2}$

$\text{i}=0.6(1-{\text{e}}^{\frac{-10\ell \text{n}\sqrt{2}}{5}})=0.6(1-e^{\ell nx{\left(\sqrt{2}\right)}^{-2}})=0.3$

$i=i_0(1-e^{\frac{-Rt}{L}})=0.6(1-{\text{e}}^{\frac{-10t}{5}})$

$\frac{di}{dt}=i_0(-(-2\left)e^{-2t}\right)=0.6\times 2e^{-2t}=1.2e^{-2t}$

Emf across coil $=L\frac{di}{dt}=5\times 1.2e^{-2t}=6{\text{e}}^{-2\ln \sqrt{2}}=3V$

Hence, emf across coil is $3V$