## Measurement of the Time Constant in an RC Circuit
In this lab experiment we will measure the time constant τ of an RC circuit via
three different methods. In figure 1 we've sketched a series RC circuit. Figure 1 - Diagram of an RC CircuitWhen the switch is in position 1, the voltage source supplies a current to the resistor and the capacitor. Charge is deposited on the plates of the capacitor. At first there is very little charge on the plates, however, as time goes on the charge on the plates builds up and the increased voltage across the capacitor will reduce the flow of current through the circuit. We can see this in the following loop equation:
V As q gets larger, i must get smaller to compensate. As time goes on, the current will eventually approach zero. When the switch is moved to position 2, the battery is removed from the circuit, and the charge that has built up in the capacitor flows through the resistor. In this case the equation is:
iR + q/C = 0
This first order differential equation has a solution in the form of an exponential:
Where τ = RC. This decaying function is plotted in figure 2: Figure 2 - Exponential DecayGiven the values of R and C in most circuits, it is very hard to "watch" the decay. In this lab we will cheat a little bit, we will connect our RC circuit not to a voltage supply with a switch, but to a function generator that is outputting a square wave. This will act as an "on" and "off" voltage supply hundreds or thousands of times per second. We can then observe the voltage across the circuit on an oscilloscope, and measure τ from there.
On your breadboard connect a capacitor and resistor in series. Pick a pair with an RC of 10
Figure 3 - Photo of RC Circuit
On your scope inspect the voltage across the capacitor. It should look something like Figure 4. Figure 4 - Top: Diagram of Voltage Response Bottom: Voltage across the Capacitor on the OscilloscopeExtend the period of the function generator so that it looks like the capacitor is fully discharging. "Blow up" this section of the graph by changing the time scale, this way you can inspect it more closely. See Figure 5. Figure 5 - "Blow Up" of the decaying part of the waveform
Our second method of measuring the time constant will be a "one point" measurement. Since e
In your conclusion discuss the RC circuit, compare your values for τ with their uncertainties, and include your thoughts on the best way to measure τ. Note that you conclusion should be decently longer than ones you have written so far for this class, and that if your discussion does not include comments upon the uncertainties in your measurements, it will not be considered complete. |