# Parallel Plate Capacitor

A capacitor consists of two conducting plates separated by an insulator and is used to store electric charge. If a voltage is applied to the capacitor, one plate becomes negatively charged and the other becomes positively charged.

For a plates where d<< A, the capacitance C  is given by:

C = ε0 A / d

where A is the area each plate, d is the separation of the plates, and ε0 is the permittivity of freespace (= 8.854X10-12).

For the Pasco parallel plate capacitor, A = π (0.085 m)2 = 2.27X10-2  m2

and d = 1.5X10-3 m for the minimum plate separation.  Therefore,

Ctheorey = 1.34X10-10 F  or 0.134 nF

As you move the right-hand plate farther away from the fixed plate, the capacitance varies as 1/d, so it falls rapidly and then remains fairly constant after about 3 cm.

Two different measurements can be made as demonstrations:

1.  A digital multimeter with a capacitance range can be connected across the capacitor (Fig. 1 below).  The meter itself provides the charging current, measures the potential difference, and converts it to a capacitance value.  If the plates are set to their minimum separation, the meter will read about:

Cmeasured = 0.33 nF

This measurement is about a factor of two higher than the calculated capacitance value and can be "hand-wavingly" explained by the addition of edge effects since the plates are covered with conducting metal all over (edges and backs), adding capacitance to the measurement that is not included in the calculated value.

Also note that the inexpensive digital capacitance meter used in this demonstration has no way to compensate for test lead capacitance.Using a more sophisticated impedance meter yields Cmeasured = 0.27 nF.

You can increase the plate separation and note that the decrease in the measured capacitance varies with 1/d.

2.  Instead of a capacitance meter, a separate power supply can be used to charge the plates and an electrometer to measure the voltage across the plates.

Connect the equipment as shown in Fig. 2 below.

Set the fixed plate on the left at the 0 distance position.  The scale on the optical bench will then read the actual plate separation in cm. Set the moveable plate on the right to the minimum separation, 0.15 cm.

Attach the black lead from the electrometer to the moveable plate and the black (ground) lead from the power supply to the ground jack on the side of the electrometer.

Attach the red lead from the electrometer and the red (positive lead with the alligator) from the power supply to the fixed plate.

With the power supply turned off and the voltage turned to 0, set the electrometer RANGE to 10 volts and turn it on.

Press the ZERO button on the electrometer to remove any residual charge.

Switch on the power supply and slowly turn up the voltage until the electrometer shows 5 volts.  Then disconnect the alligator clip.  The electrometer should still show 5 volts if you do not move around very much – you may want to move your hand just enough to disconnect the alligator clip but not move farther than a few centimeters from the terminal.

Change the electrometer RANGE switch to 100 volts.  Move the moveable plate to 0.5 cm separation and note the electrometer voltage. Make sure you do not touch the metal-plated part of the plate.  Change the plate separation to 1.0 and note the voltage. Continue to increase the plate separation in steps of 1.0 cm up to about 10.0 cm (Fig. 3 below).  Return the moveable plate to the minimum 0.15 separation; the voltage should return to 5 volts.

Since Q = CV and the charge remains constant during the plate separation changes, if the capacitance C decreases as 1/d, then the voltage V across the plates must increase as 1/d.

Acrylic dielectric plates can be inserted between the conducting plates to increase capacitance.  The dieliectric plate must be free of charge to start with and should not touch the metal plates as it is inserted so that additional static charge is not created.   