Question

A coil of resistance $400\, \Omega$ is placed in a magnetic field. If the magnetic flux $\phi \, (Wb)$ linked with the coil varies with time t(sec) as $\phi=50\, t^2+4$. The current in the coil at $t = 2\, \sec$ is

• A. 0.5 A
• B. 0.1 A
• C. $2 A$
• D. $1 A$

Answer 1

Answer: (A)

Here, $\phi=50\, t^{2}+4 W b,\, R=400\, \Omega$
Induced emf, $\varepsilon=-\frac{d \phi}{d t}$
$=-\frac{d}{d t}\left(50 t^{2}+4\right)=-100\, t\, V$
At $t=2 s, \varepsilon=-200\, V$
$|\varepsilon|=200\, V$
Induced current in the coil at $t=2 s$ is
$I=\frac{|\varepsilon|}{R}=\frac{200 V}{400 \Omega}=\frac{1}{2} A=0.5\, A$