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 VDc 0.5 volts Steps: 1) Write the differential equation for the circuit after the switch is closed. The DC 2) Approximate the differential equation with a finite difference equation. Use the first order forward difference equation dt stepsize to approximate the derivative. Numerically solve the above difference equation for Vc(it1) 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 of0.1 seconds. Use the following values of R and C 10,000 ohms, C = 0.0002F 5,000 ohms, C = 0.0001 F a) R b) R 2) Use a simulation time step of 0.5 seconds. Use the following values of R and C a) b) R = 10,000 ohms, C = 0.0002E R = 5,000 ohms, C = 0.0001 F 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 VDc 0.5 volts Steps: 1) Write the differential equation for the circuit after the switch is closed. The DC 2) Approximate the differential equation with a finite difference equation. Use the first order forward difference equation dt stepsize to approximate the derivative. Numerically solve the above difference equation for Vc(it1) 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 of0.1 seconds. Use the following values of R and C 10,000 ohms, C = 0.0002F 5,000 ohms, C = 0.0001 F a) R b) R 2) Use a simulation time step of 0.5 seconds. Use the following values of R and C a) b) R = 10,000 ohms, C = 0.0002E R = 5,000 ohms, C = 0.0001 F