Procedure & Analysis
1. Set-up the circuit as shown in Figure A. Connect the CBL / Data Logger Unit across the capacitor
using a voltage probe. Connect the positive lead of the voltage probe to the positive terminal of the
capacitor. Note that the positive terminal of the capacitor must be connected to the positive
terminal of the 10 volt battery / DC Power Supply. If the connection is reversed, the capacitor will
be permanently damaged.
2. Set-up the CBL / Data Logger Unit to read on a 0 to + 15 V scale and a continuous time scale
from 0 to 40 seconds.
3. Throw the SPDT switch into the DC Power Supply position (position 1) to charge the capacitor to
10 volts. Allow the capacitor to charge for 1-2 minutes.
4. Start the CBL / Data Logger Unit to begin recording the voltage across the capacitor and throw the
SPDT switch into the 47 Ω position (position 2). Record the capacitor voltage every second over
the 0-40 second time interval and record in the data table below.
5. Plot the voltage as a function of time on graph paper, with the voltage on the y-axis, and the time
on the x-axis.
6. The voltage will decrease using an exponential decaying function of the form:
Vc = V0 e
−
t
τ
Where V0 is the initial power supply voltage of 10 volts, and τ represents a decay constant, called
the time constant for this RC circuit and is calculated as:
τ = RC (s)
The time constant is the time required for the current to decrease by a factor of e −1 , or 36.8% of it
peak value.
7. Calculate the current through the capacitor, for each voltage recorded in the table, using Ohm’s
Law and plot the current as a function of time on graph paper as:
t
V −
I c = c e τ where R = 47Ω
R
8. Using the current tabular data accumulated above, perform a numerical regression using above
exponential model.
9. The total charge held between the plates while the 10V was applied is discharged through the 47Ω
resistor, when the SPDT switch is placed in position 2, and is observed as an exponentially
decreasing current. Therefore, the area under the current curve, represents the total charge that was
initially stored in the capacitor.
I=
dQ
dt
or
40
Q = ∫ Idt (Coulombs)
0
Then the capacitance can be calculated as:
C=
Q
, where Q is the total charge on the capacitor, and V = 10V
V
Data Table
Time (s)
Voltage (V)
Current (I)
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
20
30
40
Conclusion
1. Compare the value of capacitance calculated with the label value on the capacitor. Calculate the
percent error. How close did the calculated value of capacitance come to the actual label value? A
typical capacitor has a tolerance of 20-30% of it’s label value.
2. Without the series resistance of 47Ω, how fast would the capacitor discharge?