1. Capacitor-Resistor Circuits
In-class activity:
In pairs build this circuit in Multisim.
Look at the voltage across the capacitor on the oscilloscope.
Describe what you see when the switch moves between positions (let the switch stay in each position until the capacitor voltage stops changing).

2. Discharge of a Capacitor Through a Resistor
In the following circuit, when the switch moves from the battery to the wire connected to ground, the voltage across the capacitor is vc(t) = Vse-t/RC Vs vc -

3. Class Activity What are the units of RC in vc(t) = Vse-t/RC ?
Since vc(t) = Vse-t/RC and , what is i(t) in terms of Vs, R and C?
What do vc(t) and i(t) look like on a graph?

4. Step Response: RC Time Constants
Now, what happens when the switch moves the other way? Vs
The response of the capacitor voltage will be to charge up to the supply voltage.

5. Vc Response to Constant Voltage Vs
The voltage across the capacitor will rise and asymptotically approach Vs
How can we describe this mathematically?

6. Analysis of RC CircuitsVs vc
Kirchhoff’s voltage loop law
Ohm’s law across resistor
Substituting for VR gives

7. Analysis of RC CircuitsVs vc
From previous page
Substitute in for i

8. Analysis of RC Circuits
The equation is called a differential equation.
The solution is of the form: where is defined as the time constant
 = the circuit time constant, in seconds if and only if C = the total (connected) capacitance Farads
R = the total (connected) resistance Ohms

9. Team Activity
Substitute into the equation
to show that LHS = RHS

10. Team Activity
Show that when t is 5 times the time constant, , the capacitor voltage is 99.33% of the peak voltage.

11. Team Activity – Discharge Process
Kirchhoff’s voltage loop law ?
Ohm’s law across resistor?
Substituting for VR gives?

12. Team Activity From previous activity the equation Substitute
into the above equation
and show that LHS = RHS

13. Rectangular Wave
If you repeatedly switch between the battery and the short you are effectively applying a rectangular time pulse to the RC circuit. 13

14. Rectangular Wave Response
The voltage across the capacitor will behave as below in response to such a wave: 14