A circuit consists of a 36 V battery connected in series with a 3 resistor and a switch. After the switch, the circuit splits into two parallel branches: one contains an unknown resistor R , and the other contains a 6 resistor in series with an inductor L . A long time after closing the switch, the steady-state current through the battery is 6 A . The current through the battery just after closing the switch is _____

Step-by-step solution

Let the unknown resistance be R . A long time after closing the switch, steady state is reached and the inductor behaves as a short circuit. The 6 resistor and resistor R are in parallel, and this combination is in series with the 3 resistor. The equivalent resistance of the circuit is: R_ eq = 3 + 6R 6 + R Using Ohm's law for the steady-state current: I = V R_ eq 6 = 36 3 + 6R 6 + R 3 + 6R 6 + R = 6 6R 6 + R = 3 6R = 18 + 3R 3R = 18 R = 6 Just after closing the switch (at t = 0 ), the inductor behaves as an open c