Experiment 6: MEASURING THE TIME CONSTANT OF AN RC CIRCUIT
Object: The object of this experiment is to study the behavior of the time dependent potential
difference across a capacitor in a simple RC series circuit.
Prior to Lab: From the information in the discussion immediately below, write the equations for
the time dependence of the voltage across the capacitor when it is
a. charging and
b. discharging.
Discussion: When a capacitor is charged through a resistor the charge builds up exponentially
to its maximum, Q according to the equation
q = Q(1-e-t/τ)
where τ = RC, Q = CV and Qo = CE with E = VC(max). τ is called the time constant and equals
the time required for the charge (and voltage) to build to 0.63% of its maximum. A capacitor
that is originally charged with a charge Qo discharges according to the equation
q = Qoe-t/τ.
where τ, the time constant, equals the time required for q to equal 0.37% of its original value.
For a full discussion of the theory of an RC series circuit, see your textbook.
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The circuit provided has a large enough time constant that data may be taken using a timer and
voltmeter. The data can then be graphed, and the shape of the graph and value of the time
constant may then be investigated. The time constant can then be compared to the theoretical
value obtained by computing RC from the resistor and capacitor used to perform the experiment.
V
C
+
R
2
1
S
E
Figure 1. Wiring diagram for charging and
discharging an electrolytic capacitor (C) in and
RC circuit. V is the voltmeter. Switch (S) in
position 1 is for charging and switch in position
2 is for discharging.
Figure 2. The apparatus wired as according to
the wiring diagram on the left. An additional
(white) wire is attached between the capacitor
and resistor to speed up the experiment.
PROCEDURE:
1. Wire the circuit according to the diagram provided in Figure 1. Warning: Pay particular
attention to the polarity of the wiring, you are using an electrolytic capacitor which, if wired
backwards will leak a measurable current (you will get an incorrect result) and may be
damaged! Your instructor will check your circuit and set the source voltage to 10
volts.
2. Discharge the capacitor (short circuit it).
3. Simultaneously start the timer and close the switch (position 1) to complete the charging
circuit. Keep the switch closed, and record voltages every 10 seconds for at least 2.0 time
constants (200 seconds).
4. When you are finished taking data, short circuit the resistor to fully charge the capacitor to E.
Record this value.
5. Simultaneously start the timer and close the switch (position 2) to complete the discharging
circuit. Keep the switch closed, and record voltages every 10 seconds for at least 2.0 time
constants (200 seconds). (NOTE: The voltage at t = 0 will be the initial voltage for
discharging the circuit.)
6. Repeat steps 2 through 5 at least once more to verify the consistency of your data.
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7. Analysis
a. Charging data:
Plot a graph of V vs. t. Calculate VC(max) - V. Plot a second graph of (VC(max) – V) vs. t
and determine the exponential trendline of the second graph to determine E and the
time constant τ.
b. Discharging data:
Plot a graph of V vs. t. Determine the exponential trendline of the graph to determine E
and the time constant τ.
8. Use the measurement uncertainty formula for your DMM to determine the uncertainty of your
measured value of Vmax. Is the trendline coefficient of the exponential from 7a within the
range determined by Vmax ± ΔVmax?
9, Repeat 8 for 7b.
10. Compare with the product of RC for your apparatus with the value of τ determined from of
each of your trendlines. Include the uncertainty of the product RC using the manufacturer’s
tolerances for the values of R and C. The manufacturer’s tolerances are 10% for R and C. Is
your measured time constant within the range of the uncertainty you calculated?
11. Discuss any sources of error in your conclusion.
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