Question

Flux $(\phi)$ (in weber) in a closed circuit of resistance $20 \,\Omega$ varies with time $t$ (in second) according to equation $\phi=6 t^{2}-5 t+1$. The magnitude of the induced current at $t=0.25 \,s$, is

• A. $1.2\, A$
• B. $0.8 \,A$
• C. $0.6 \,A$
• D. $0.1 \,A$

Answer 1

Answer: (D)

From Faraday's second law, $e=-\frac{d \phi_{B}}{d t}$
$=-\frac{d}{d t}\left(6 t^{2}-5 t+1\right)=-(12 t-5)$
At $t=0.25\, s =-[12 \times(0.25)-5]=+2 V$
Now, $i=\frac{e}{R}=\frac{2}{20}=0.1\, A$