Project 4 Consider the following circuit, with R = 20. R Assume first that v, = 12V-u(-t) and X is a capacitor with C = 25mF. + (a) What is the initial energy stored in the capacitor? i x v (b) Write an expression for the voltage v as a function of time, then Us compute v at t = t, 2t, and 3r. (c) Write an expression for the current i through the capacitor as a function of time, then compute i at the same three instants of time. (d) Write an expression for the power delivered by the capacitor as a function of time. At what time is the power delivered maximum? What is the value of the power delivered at that time? (e) Sketch voltage, current, and power delivered vs. time from t = 0 tot = 10t. (f) Integrate your expression for power delivered to show that the total energy delivered by the capacitor is exactly equal to the initial energy stored. Assume now that v, = 12V-u(t) and X is an inductor with L = 50mH. (g) What is the final energy stored in the inductor? (h) Write an expression for the current i as a function of time, then compute i at t = t, 2t, and 3t. (i) Write an expression for the voltage v across the inductor as a function of time, then compute v at the same three instants of time. (j) Write an expression for the power absorbed by the inductor as a function of time. At what time is the power absorbed maximum? What is the value of the power absorbed at that time? (k) Sketch current, voltage, and power absorbed vs. time from t = 0 to t= 107. (1) Integrate your expression for power absorbed to show that the total energy absorbed by the inductor is exactly equal to the final energy stored.