Question

To understand the dynamics of a series R-C circuit.

Consider a series circuit containing a resistor of resistance R and a capacitor of capacitance Cconnected to a source of EMF E with negligible internal resistance. The wires are also assumed to have zero resistance. Initially, the switch is open and the capacitor discharged. (Figure 1)

Let us try to understand the processes that take place after the switch is closed. The charge of the capacitor, the current in the circuit, and, correspondingly, the voltages across the resistor and the capacitor will be changing. Note that at any moment in time during the life of our circuit, Kirchhoff's loop rule holds and, indeed, it is helpful: E?VR?VC=0, whereVR is the voltage across the resistor and VC is the voltage across the capacitor.

a. In the steady state, what is the charge

q of the capacitor?

Express your answer in terms of any or all of E, R, and C.

b. How much work

W is done by the voltage source by the time the steady state is reached?

Express your answer in terms of any or all of E, R, and C.

Answer 1

a.) Q = EC

b.) W = E^2 C