Question

For the circuit shown, steady state current supplied by battery will be?

Answer 1

To find:

Current supplied by the battery in a steady state.

Calculation:

At steady state , an inductor acts like a plain wire and doesn't provide any resistance.

Hence , after assigning potential drops to each resistance the simplified circuit can be drawn as :(Refer to attached diagram)

So, left( 4R and 12R) are in parallel combination;

$R1 = ( \dfrac{4 \times 12}{4 + 12}) R= 3 R$

Again right (4R and 12R) are in parallel combination;

$R2= (\dfrac{4 \times 12}{4 + 12} )R= 3 R$

So, equivalent resistance of circuit:

$R_{eq.} = R1 + R2 = (3 + 3)R = 6R$

So, net current in steady state:

$\therefore \: i = \dfrac{voltage}{R_{net}}$

$= > i = \dfrac{E}{6R}$

So, final answer is:

$\boxed{ i = \dfrac{E}{6R} }$