Magnetic flux (in weber) in a closed circuit of resistance 20   Ω varies with time t s as ϕ =…

Given that magnetic flux $\varphi =8t^2-9t+5$

According to Faraday's law of electromagnetic induction

$\mathrm{emf}=-\frac{\mathrm{d}\varphi }{\mathrm{d}t}=-\left(16t-9\right)$

At $t=0.25 s$

$\mathrm{emf}=-\left[\left(16\times 0.25\right)-9\right]=5 \mathrm{V}$

Current $=\frac{\mathrm{emf} }{ \mathrm{Resistance} }=\frac{5 \mathrm{V}}{20 \mathrm{\Omega }}$

$=\frac{1}{4} \mathrm{A}=\frac{1000}{4} \mathrm{mA}=250 \mathrm{mA}$