3. RC Circuit [25 points] Consider the RC circuit in Figure 1. in R Figure 1. Circuit for Problem 3 a) Write the transfer function between the input voltage and the output voltage. Hint: This equation was derived in class. b) Let R=200 and C=500 μF. Find the static sensitivity and time constant of this first-order system. c) Suppose the voltage source acts as a step input signal, jumping from V, =0 V to V, 15 V at time t=0 s. Using the resistance and capacitance values from part (b), find the value of the output voltage at time t=0.2 s. Assume that no energy is stored before the step is applied.

Fig: 1