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# RC Circuits

"A fact is a simple statement that everyone believes. It is innocent, unless found guilty. A hypothesis is a novel suggestion that no one wants to believe. It is guilty, until found effective"
Edward Teller

## CHARGING

- An example of a series RC circuit is shown at right. With the emf included in the circuit, applying the loop theorem we find

> where q/C is the voltage drop across the capacitor and i is the current in the circuit.

- Using the fact that i = dq/dt, we obtain

- This is a "simple" differential equation the solution of which can be written

> or

- The voltage across the capacitor, VC = q/C and the voltage across the resistor, VR = iR. Using the equations above we find that the dependence of these voltages on time is shown below

- Note that the time on the horizontal axis is measured in units of τ = RC, the capacitative time constant.

- After one time constant VC has reached 63% (1 - e-1) of its maximum value and VR has 37% (1/e) of its final value.

## DISCHARGING

- Now switch the emf out of the circuit and reapply the loop theorem

> which gives
> which has the solution
> and
> where Cε is the initial charge on the capacitor and ε/R is the initial voltage across the capacitor.

- The time dependence of VC and VR (where VR is proportional to the current in the capacitor) are shown at right.

- Once again the time axis is measured in units of RC.

- After one time constant VC has decreased to 37% (1/e) of its initial value and |VR| has decreased to 37% (1/e) of its initial value.

Q: What did one quantum physicist say when he wanted to fight another quantum physicist?
A: Let me atom.

Dr. C. L. Davis
Physics Department
University of Louisville
email: c.l.davis@louisville.edu