Question

A coil having resistance $20\Omega$ and inductance $2H$ is connected to a battery of emf $4.0V$. Find (a) the current at $0.20s$ after the connection is made and (b) the magnetic field energy in the coil at the instant

Answer 1

$L=2HR=20\Omega emf=4Vt=0.20s$

$I_0=\frac{e}{R}=\frac{4}{20}=0.2$

$t=\frac{L}{R}=\frac{2}{20}=0.1$

$\left(a\right)$

$I=I_0(1-e^{-0.2/0.1})=0.17A$

$\left(b\right)$

$\frac{1}{2}L{I}^2=\frac{1}{2}\times 2\times {0.17}^2=0.03J$