In the circuit shown in the figure below, the direct current (DC) voltage supply V = 10.0 V, R = R2= 4.00 12, R3=8.00 22 and L = 1.00 H. At time (), switch S is closed. = R1 W R3 W + R2 La (a). After S is closed for a very long time, the circuit reaches a steady state. What is the steady- state current that flows through the inductor L? [5 marks] (b). After the circuit reaches the above steady state, switch S is open. How does the current of the inductor change? What is the time constant? [5 marks] (c). What is the time constant of the circuit at time 0 when S is closed? (Challenging question. Hint: Start by finding the relationship between the current flow in the different resistors and inductor, and then compare the equation that you get with the standard inductor charging equation that we have discussed in class). [8 marks]