Question

Magnetic flux (in weber) in a closed circuit of resistance $20 \,\Omega$ varies with time $t ( s )$ as $\phi=8 t^2-9 t+5$. The magnitude of the induced current at $t =0.25\, s$ will be ______$mA$

Answer 1

$ \phi=8 t^2-9 t+5$
$ e m f=-\frac{d \phi}{d t}=-(16 t-9)$
At $t =0.25 s$
$Emf =-[(16 \times 0.25)-9]=5 \,V$
Current $=\frac{\text { Emf }}{\text { Resistance }}=\frac{5 V }{20 \Omega}$
$=\frac{1}{4} A =\frac{1000}{4} mA =250\, mA$