In the circuit shown below find the current and the voltage

In the circuit shown below, find the current and the voltage for each circuit element at the following times. Immediately after switch S is closed, and Long after the switch S has been closed.

Solution

Note rule of thumb while solving dc circuit problems is that, when an inductance is uncharged, it behaves like an open circuit and once it is charged it behaves like a wire with zero resistance

So when the switch is just closed,
current in R2 = 0 current in L = 0 current through R1 and R3 = 0.333 A = 50/150 A
Voltage across R2 = 0 and voltage through L = 16.67 V , Voltage across R1 = 33.33 V and Voltage across R3 = 16.67 V

Now, when the switch has been closed,

Current through R1 = 50 / (130) = 0.384 as R2 and R3 are now in parallel
Current through R2 = 0.384*75/125 = 0.2304 A, current through R3 = 0.384*50/125 = 0.1536 A
voltage at L = 0, Voltage across R1 = 38.4 V, Voltage at R2 and R3 = 11.6 V