Question

Learning Goal: To understand the dynamics of aseries R-C circuit.

Consider a series circuit containing a resistor of resistance R anda capacitor of capacitance C connected to a source ofEMF ε with negligible internal resistance. The wiresare also assumed to have zero resistance. Initially, the switch isopen and the capacitor discharged.

Let us try to understand the processes that take place afterthe switch is closed. The charge of the capacitor, the current inthe circuit, and, correspondingly, the voltages across the resistorand the capacitor will be changing. Note that at any moment in timeduring the life of our circuit, Kirchhoff's loop rule holds and,indeed, it is helpful: ε-V_R -V_C =0,where V_R is the voltage across the resistor andV_Cis the voltage across the capacitor.

a)

In the steady state, what is thecharge q of the capacitor?

Express your answer in terms of anyor all of ε, R, and C.

B)

How much work W is done by the voltage sourceby the time the steady state is reached?

Express your answer in terms of anyor all of ε, R, and C.

Answer 1

a)

q = Cε

b)

W= Cε^2