Design TWO experiments to determine the capacitance of an unknown capacitor usin

Question

Design TWO experiments to determine the capacitance of an unknown capacitor using ONLY the following equipment: 10 or 50 resistor, unkown capacitor, switch, power supply, voltage probe, computer, connecting wires, capacitance analyzer.

For each experiment: Sketch a circuit to use (hint: using a discharging circuit may be more convenient than a charging circuit in terms of future calculations), write down the theory or mathematical model to be used and describe what you will do, including what physical quantities to be measured and how they will be measured. Include any assumptions and sources of uncertainty in your designs.

Explanation / Answer

Make an RC discharging circuit.

Connect capacitor with unknown capacitance C in series with a DC power supply and a resistor with resistance R. Connect a voltmeter across the Resistor.

Switch on the circuit and let the capacitor charge upto the source voltage Vo . This can be ensured by waiting for reasonably long time.

Now remove the power supply from the circuit while still maintaining the connection between other components. The capacitor now discharges. The voltage across the resistor will drop. This drop is given by:

V = Voe-t/RC

or, ln(Vo/V) = t/RC

=> C = t/R ln(V/Vo)

now, measure the initial and final values of voltage across the resistor at different time t.

use this relation to find the capacitance C.

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