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Physics 261
Capacitors
Introduction
Capacitors, a pair of conductors separated by a dielectric (insulator), store charge (or equivalently,
the energy required to form an electric field between the conductors). The quantity of charge Q
stored depends on the applied potential difference V and the nature of the capacitor:
Q = CV
(1)
The nature of a capacitor–its shape, layout, elements–is summarized in the term C, the capacitance:
charge per unit potential difference. In standard international units, capacitance is measured in
farads = coulombs / volt. One coulomb is a great deal of charge, so one ordinarily encounters
capacitances in the micro-, nano-, or pico-farad range.
You will quantitatively determine the effect of separation between two parallel conducting plates
on the capacitance of the pair when air is the dielectric, and qualitatively determine the effect of
replacing air with plastic. You will also determine what happens to the total capacitance when two
capacitors are connected in series and in parallel.
Capacitance Meter
Because the capacitance, just as the resistance and inductance, is affected by configuration, to measure its value in a single component requires that the component be isolated. Wires and other
components all increase or diminish the capacitance depending how they are attached to the component of interest. It may be possible to determine their effect and correct for it, but, again, isolation
is best.
The capacitance meter you will use has an adjustment knob that allows one to zero the meter
when nothing is connected. After you set the range with the rotary switch, be sure to zero the
meter before inserting the capacitor. Capacitors with plugs should be inserted in the Cx and COM
recepticals; those with just posts or wires can be inserted in + − slots.
Meter measurements have well-defined intrinsic uncertainties (see Table ).
Capacitance Measurement Uncertainties of Meterman CR50.
Capacitance Range
Accuracy
200 pF
±0.5% + 1 lsda +0.5 pF
2 nF to 2 µF
±0.5% + 1 lsda
20 µF
±0.5% + 1 lsda
200 µ F
±0.5% + 1 lsda
2 mF
±1.0% + 1 lsda
20 mF
±1.5% + 1 lsda
a in
the place of lsd (least significant digit)
Let’s say, on the 200 pF scale, you get a reading of 147 pF. To find the uncertainty, you note
from the table that the reading is accurate to 0.5% plus 1 in the place of the least significant digit
(here, the ones’ place) + 0.5 pF, so that the uncertainty is (.005)(147) + 1 + 0.5 = 2.235 pF, so the
reading is (147 ± 2) pF. Keep and understand this information for future reference; you don’t need
it in this experiment, but you will in later ones.
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Relationship Between Parallel Plate Separation and Capacitance
• Adjust screws to ensure plates are parallel.
• Use the most sensitive range of the multimeter.
• Keep cables short and in approximatedly the same position throughout the measurements.
• Determine the inherent capacitance of the setup (C0 ) by measuring it with the plates at
maximum separation.
• In steps of 0.5 cm, measure capacitance of system when plates are separated from 0.5 cm to
3.0 cm. Don’t worry about uncertainties.
• Determine the relationship between separation of the plates and capacitance.
Effect of Different Dielectrics
• Press the plates up against two sheets of plastic and measure the capacitance.
• Without moving the plates, remove the plastic and measure the capacitance.
• What’s the difference?
Capacitors in Series and in Parallel
• Assemble one nominal 0.022 µF capacitor and one nominal 0.0152 µF capacitor in series and
measure the capacitance of the system.
• Assemble the same capacitors in parallel and measure the capacitance.
• Suggest formulae for combining capacitors.