Two concentric circular coils, C _ 1 and C _ 2 , are placed in the...

$I = \left(5{t}^{2} + 2t + C\right)$

$\dfrac{di}{dt} = ( 10t + 2 )$

${ϕ}_{\text{small}} = BA = \left(\dfrac{{\mu}_{0}I{N}_{2}}{2R}\right)\left(\pi{r}^{2}\right)$

induced emf in small coil

$e = \dfrac{dϕ}{dt} = \left(\dfrac{{\mu}_{0}{N}_{2}}{2r}\right)\pi{r}^{2}{N}_{1}\dfrac{di}{dt} = \left(\dfrac{{\mu}_{0}{N}_{1}{N}_{2}\pi{r}^{2}}{2R}\right) ( 10t - 2 )$

at $t = 1$

$e = \left(\dfrac{{\mu}_{0}{N}_{1}{N}_{2}\pi{r}^{2}}{2R}\right)8 = 4\dfrac{{\mu}_{0}{N}_{1}{N}_{2}\pi{r}^{2}}{R} = \dfrac{4 ( 4\pi ) {10}^{- 7} \times 200}{20} \times 500 \times \dfrac{{10}^{- 4}}{{10}^{- 2}}\pi$

$= 80 \times {\pi}^{2} \times {10}^{- 7} \times 10 \times {10}^{2} \times {10}^{- 2} = 8 \times {10}^{- 4}volt = 0 . 8mV = \dfrac{4}{x}$

$x = 5$