Vdc R Vc Write a program that calculates the capacitor voltage after the switch is closed. The capac- itor is initially uncharged. Perform the simulation for a duration of five seconds. Use Voc= 0.5 volts Steps: 1) Write the differential equation for the circuit after the switch is closed. The equation should be in terms of R, C, Vc, and Voc 2) Approximate the differential equation with a finite difference equation. Use the first order forward difference equation dV dt V(i+1)-V(i) stepsize to approximate the derivative. Numerically solve the above difference equation for Ve(i+1). 3) Write a C program that iterates the difference equation and prints out the voltage at each time instant. Analysis: 1) Use a simulation time step of 0.1 seconds. Use the following values of R and C a) R 10,000 ohms, C = 0.0002F b) R 5,000 ohms, C=0.0001F 2) Use a simulation time step of 0.5 seconds. Use the following values of R and C a) R b) R 5,000 ohms, C=0.0001F 10,000 ohms, C = 0.0002F