Question

Two concentric circular coils, $C_1$ and $C_2$, are placed in the $XY$ plane. $C_1$ has $500$ turns, and a radius of $1cm$ . $C_2$ has $200$ turns and radius of $20cm$ . $C_2$ carries a time dependent current $I(t)=\left(5t^2-2t+3\right)$ A where $t$ is in s. The emf induced in $C_1$ (in $mV)$, at the instant $t=1s$ is $\frac{4}{x}.$ The value of $x$ is _____.

Answer 1

Answer: 5.00

$I=5t^2-2t+3$
$\frac{dl}{dt}=10t-2$
$\text{ At }(t=1sec)\left(\frac{dl}{dt}\right)=8A/s$
$\varphi =\left(\frac{{\mu }_0\times 200\times 1\times 100}{2\times 20}\right)\times \frac{\pi \times 500}{100\times 100}$
$\therefore e=\left|\frac{d\varphi }{dt}\right|=\frac{{\mu }_0\times 200\times 100\times 500\times \pi }{2\times 20\times 100\times 100}\left(\frac{dl}{dt}\right)$
$\Rightarrow e=\left|\frac{d\varphi }{dt}\right|=\left(\frac{8}{10}\right)m\text{ volt }=\frac{4}{5}m\text{ volt }$
$x=5$