4. RL Circuit [30 points] Consider the RL circuit in Figure 2. R Vout in Figure 2. Circuit for Problem 4 a) Derive the differential equation for the current as a function of the input voltage. b) Find the transfer function between the input voltage and the current (output). c) Does the transfer function in part (b) act as a first-order system? If so, find its static sensitivity and time constant if R = 10 and L = 500 mH. d) Suppose the voltage source acts as a step input signal, jumping from V₁ =0 V to V, = 15 V at time t=0 s. What is the steady-state value of the current in response to this step input (i.e., the value of I(t) as t→co) for the resistance and inductance values from part (c)? e) Using the resistance and inductance values from part (c), find the value of the current at time =0.2 s for the step input above. Assume that no energy is stored before the step is applied.

Fig: 1