Question

Fill in the blank.
A uniformly wound solenoid coil of self inductance $1.8\times {10}^{-4}$ Henry and resistance $6\Omega$ is broken into two identical coils. These identical coils are then connected in parallel across a $12-volt$ battery negligible resistance. The time constant for the current in the circuit is .......... $sec$ and the steady state current through the battery is .......... $amp.$

Answer 1

Net $I=\frac{0.9}{2}\times \frac{1}{{10}^4}=\frac{0.45}{{10}^4}$

$=\frac{4.5}{{10}^5}$H

Net $R=\frac{3}{2}=1.5\Omega$

$T=\frac{L}{R}=\frac{4.5}{{10}^5}\frac{3}{1.5}=3\times {10}^{-3}$s

Steady current$=\frac{V}{R}=\frac{12\times 4}{3}=8$A.