An ideal battery of emf V is connected in series with a switch, a resistor of resistance R , and a network of three identical inductors (each of inductance L ). The inductor network consists of two inductors connected in parallel, which are then connected in series with the third inductor. The switch is closed at t=0 . Neglecting mutual inductance, what is the initial rate of change of current drawn from the battery

Step-by-step solution

At t=0 , immediately after the switch is closed, the current in the circuit is zero ( I = 0 ). The voltage drop across the resistor is V_R = IR = 0 . Therefore, the entire battery emf V appears across the equivalent inductance of the network. The equivalent inductance L_ eq of two inductors in parallel is L 2 . This combination is in series with the third inductor, so the total equivalent inductance is: L_ eq = L + L 2 = 3L 2 Using the relation V = L_ eq dI dt , the initial rate of change of current is: dI dt = V L