LAB 5
Capacitors
OBJECTIVES
1. Predict and measure the unknown capacitance CX for various series and parallel
combinations.
2. Predict and measure the voltages and equivalent capacitance across capacitors in
series and parallel.
EQUIPMENT
Capacitors (two each: 0.05 µF, 0.10 µF; and one 0.22 µF), electrometer, DC power supply,
DMM, breadboard.
THEORY
Any arrangement that stores charge can properly be called a capacitor. The capacitance of
a capacitor is a measure of how much charge can be stored on the capacitor for a given
potential difference (voltage). The relation between charge q, voltage V, and capacitance C
is given by:
q = CV.
When two or more capacitors are connected together, they may be replaced by a single
capacitor that has the same capacitance (Ceq) as the combination of capacitors. For two
capacitors connected in parallel, the equivalent capacitance is given by:
Ceq
= C1 + C2 .
For two capacitors connected in series, the equivalent capacitance is given by:
1/=
Ceq 1/ C1 + 1/ C2 .
If a capacitor C1 is connected to a power supply with voltage V0, it will acquire a charge q
given by q = C1V0. If that capacitor is then disconnected from the power supply and
connected in parallel to an initially uncharged capacitor C2, the original charge q on
capacitor 1 is split between the two capacitors. We therefore end up with the relation q = q1
+ q2, where q1 and q2 are the final charges on capacitors 1 and 2. Since capacitors 1 and 2
are in parallel, they must have the same voltage V. The relationship q = q1 + q2 therefore
becomes C1V0 = C1V + C2V.
PROCEDURE
Part 1: Measuring the Unknown Capacitance CX
a. Measure the individual capacitance values (using a DMM) of the following two
capacitors: 0.05 µF and 0.1 µF.
b. Before you make any mathematical calculations or experimental measurements, rank
the equivalent capacitance of the four combinations list below from highest to lowest
values. Explain your reasoning.
c. Using the measured capacitance values, predict the unknown capacitance (CX)thy by
combining
i. 0.05 µF and 0.10 µF in series with the CX
ii. 0.05 µF and 0.10 µF in parallel with the CX
iii. A combination of 0.05µF in parallel with 0.10 µF and in series with CX
iv. A combination of 0.05µF in series with 0.10 µF and in parallel with CX
Average these four values to obtain (CX)thy.
d. Measure the unknown capacitance (CX)expt using the DMM and compare it with the
averaged (CX)thy using a percent difference. How do they compare?
Part 2: The Voltage across Capacitors
To measure the voltage across an initially uncharged capacitor, use the following procedure:
• Connect a 0.05 µF capacitor to a 10V power supply and charge it up (one or two
seconds). Disconnect the power supply from the capacitor and be careful not to touch
either side of the capacitor or you will discharge it. Check the voltage of the capacitor
and power supply using a electrometer. Keep the electrometer connected across the
charged 0.05 µF capacitor. Make sure that you connect the + terminal of the
electrometer to the + plate of the 0.05 µF capacitor, otherwise you will discharge the
capacitor.
• With the charged 0.05 µF capacitor, connect a second initially uncharged capacitor in
parallel and charge it up.
• Measure the equilibrium voltage across the 0.05µF capacitor after the two capacitors is
connected in parallel. Discharge all capacitors by touching both plates of each
capacitor at the same time with your fingers.
Predict (Vthy) and measure (Vexpt) the equilibrium voltage after the two capacitors are
connected in parallel. Compare Vthy and Vexpt using a percent difference. Across the initial
0.05 µF capacitor connect the following:
a. a single 0.05 µF capacitor.
b. two 0.10 µF capacitors in parallel (make sure to use measured capacitance values).
c. two 0.10 µF capacitors in series.