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The capacitance of two unknown capacitors through the use of a circuit and oscilloscope

A capacitor consists of two conductors placed near each other but separated by an insulating material. It may take numerous forms, for example, that of a conducting sphere on an insulating stand placed in the middle of a room.

The sphere is one conductor; the walls and other objects in the room serve as the second. One of the most useful forms for a capacitor is that of two large metal sheets, close together, and separated by a thin layer of paper, oil, or other insulating material. Charges of equal magnitude and opposite sign placed on the two conductors forming the capacitor will attract each other and remain in position for long periods of time or until the two conductors are connected together via an external conducting path.

Other applications of capacitors are related with their properties in AC electrical circuits. Some of these will be shown in this experiment and, together with other electrical elements, in the RCL circuit experiment. Capacitors in electrical circuits are marked with symbol. Note that the lengths of the two vertical lines are equal in contrast of a battery symbol, where one of them is shorter than the other.

The capacitance of a capacitor is defined as the ratio of charge on one of the two conductors to the potential difference measured between the two conductors. The unit of capacitance is the farad. In most practical circuits, we are concerned with either microfarads 10-6 farad or picofarads 10 -12 farad.

The capacitance of a capacitor depends upon its geometry, i. When a capacitor is placed into a DC circuit the initial current gradually builds up charges on the conducting plates and a corresponding potential difference V is built up between them. When this potential V is equal to the voltage provided by the battery, the process stops.

In an AC circuit, the charge alternately builds up and discharges on the plates so that there is an effective current in the circuit. A capacitor in AC circuits represents a barrier of the current flow, similar to a resistor. This barrier, named impedance, ZC is inversely proportional to the capacitance: This feature allows the measurement of capacitance in a bridge circuit.

The measurement of the capacitance of capacitors and that various combinations of capacitors by the bridge method is carried by using the connections as shown in Figure 1 which is the same as for the measurement of resistance with the Wheatstone bridge. A source of audio-frequency alternating current is used as the source in place of the DC source.

The capacitance of two unknown capacitors through the use of a circuit and oscilloscope

A cathode ray oscilloscope is used as the detector in place of the galvanometer. In the balanced condition i. Call this voltage V.

  1. A source of audio-frequency alternating current is used as the source in place of the DC source.
  2. This feature allows the measurement of capacitance in a bridge circuit.
  3. The capacitance of a capacitor is defined as the ratio of charge on one of the two conductors to the potential difference measured between the two conductors.
  4. When this potential V is equal to the voltage provided by the battery, the process stops.
  5. Since the capacitor will be charging and discharging through the same resistor, the two waveforms will be identical but inverted. Combining equations 3 and 4 , we obtain.

Combining equations 3 and 4we obtain.