Question:
In the given figure the magnetic flux through the loop increases according to the relation $\phi_{\mathrm{B}}(\mathrm{t})=10 \mathrm{t}^{2}+20 \mathrm{t}$, where $\phi_{\mathrm{B}}$ is in milliwebers and $\mathrm{t}$ is in seconds.
The magnitude of current through $R=2 \Omega$ resistor at t = 5 s is ______ mA.
Solution:
$|\epsilon|=\frac{\mathrm{d} \phi}{\mathrm{dt}}=20 \mathrm{t}+20 \mathrm{mV}$
$|\mathrm{i}|=\frac{|\in|}{\mathrm{R}}=10 \mathrm{t}+10 \mathrm{~mA}$
at $t=5$
$|\mathrm{i}|=60 \mathrm{~mA}$