See Figure below. Assume the capacitor is initially uncharged. At t=0, the switch is closed. R ww E R R +0 c Fe C= a) Suppose the switch is closed at t=0. Write down three simultaneous equations for the currents. One equation should be Kirchhoff's junction rule. The other two should apply Kirchhoff's loop rule. At least one equation will have the voltage across the capacitor, Vc. b) Write one equation in terms of current 13 and voltage Vc by using the above three equations. Hint: If you have trouble, maybe try another loop rule. c) By comparing the above equation to the one in your textbook, write down the equations for current 13, the voltage across the resistor that is above the capacitor, and the voltage Vc as a function of time. Hint: For the equation in b), what is the time constant? Review RC circuits.