Question

A coil of ${10}^{-2}H$ inductance carries a current $I=2\sin \left(100t\right)A$. When current is half of its peak value then at that instant the induced emf in coil :-

• A. $1V$
• B. $\sqrt{2}V$
• C. $\sqrt{3}V$
• D. $2V$

Answer 1

The correct option is C $\sqrt{3}V$

$I=2\sin \left(100t\right)$

$\frac{I_{max}}{2}=2\sin \left(100t\right)$

$1=2\sin \left(100t\right)$

$\frac{dI}{dt}=2\times 100\times \cos \left(100t\right)$

$=200\times \cos \left(\frac{\pi }{6}\right)$

$=200\times \frac{\sqrt{3}}{2}=100\sqrt{3}$

$ϵ=L\times \frac{di}{dt}$

$={10}^{-2}\times 100\sqrt{3}$

$=\sqrt{3}V$