Question

Magnetic flux $\varphi$ (in Weber) linked with a closed circuit of resistance$10ohm$ varies with time $t$ (in second) as $\varphi =5t^2-4t+1$. The induced emf in the circuit at $t=0.2sec$ is:

• A. $0.4V$
• B. $-0.4V$
• C. $2.0V$
• D. $20V$

Answer 1

The correct option is C $2.0V$

Given that,

Magnetic flux $\varphi =5t^2-4t+1$

Time $t=0.2\sec$

Now, the induced e. m. f in the circuit

$E=-\frac{d\varphi }{dt}$

$E=-\frac{d(5t^2-4t+1)}{dt}$

$E=-10t+4$

Now, at $t=0.2s$

$E=-10\times 0.2+4$

$E=2V$

Hence, the induced emf in the circuit is $2V$