Energy in a Capacitor

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The relationship between the energy stored in a capacitor and the voltage applied is an essential concept in A level physics. However the demonstration of this relationship is not frequently made. The two following show a traditional method which has a lot of good physics and may even be used as a class practical, and a quick reinforcing demonstration.

Using a thermocouple as a peltier heat source

This experiment is based on Ch10A190E of the OCR Spec. B “Advancing Physics” course.

Schematic for Energy in a capacitor

The Peltier-Seebeck effect is used to raise the temperature of a junction of two different metals. The temperature rise of the junction is caused by the dissipation of energy through a wire as a capacitor is discharged.
A junction is made by removing the insulation from the ends of a pair of copper wires and a single length of insulated constantan. Enamel insulation can be burnt off with a match in a well ventilated area. Cotton wound insulation can just be pushed back. The bare ends are then twisted together to form two junctions.
One junction is wrapped in a coil of thin constantan that acts as an ohmic heater. The second (usually referred to as a reference junction ) is kept at room temperature in a water bath.
The voltage produced by heating the first junction is small of the order of microvolts. However microvoltmeters are expensive and are often substituted by mirror galvanometers. These work, but require time to reset and are subject to drift. It is suggested that pupils with good manual skills only should attempt this experiment.
Beware: do not exceed the maximum working voltage of the capacitor.
Start at the maximum voltage intended to be used adjusting the scales on the meter to give the best range for resolution. The maximum deflection on the microvoltmeter should be plotted against the applied voltage on the capacitor, weighting the reading frequency toward the higher voltages.
Plot a graph of deflection (Energy) against V2 .

Apparatus to make for a quick demonstration

The demonstration apparatus requires a high value electrolytic capacitor ~1mF (modern super capacitors are ideal) and 14 identical (same batch) 1.5V bulbs and holders. The switch is not necessary.

Demonstration apparatus showing V squared relationship

The bulbs are arranged so that they form a progression of squares (1,2x2 and 3x3). The demonstration is made by charging the capacitor with one cell and then discharging through the single bulb, noting the brightness. When charged with two cells the capacitor will provide a similar brightness in each of the 4 lights in the 2x2 circuit. Again the three cells will give a similar brightness in the 3x3 matrix.

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