Part B: Suppose you make a plot of ln V_cap vs. time for a discharging capacitor

Question

Part B:

Suppose you make a plot of ln V_cap vs. time for a discharging capacitor in an RC circuit, where V_cap is in Volts and time in seconds. What does the slope of this graph represents? If the maximum voltage across the capacitor is only 75% of the voltage of the power supply (after waiting an infinite amount of time), what is the internal resistance of the voltmeter in terms of the resistor resistance R? Now, set up an RC circuit with the 5 M Ohm resistor and ~ 1mu F capacitor, and keep the power supply at 2 Volts. The time constant of this circuit is about RC 5 sec, so you should be able to see the maximum voltage across the capacitor after about 15 - 20 seconds. You will notice that the voltage across the capacitor does not seem to approach 2.0 Volts, but rather a smaller value. Measure the maximum voltage the capacitor is able to attain. Why does the capacitor not able to charge up to 2.0 Volts? From your data, estimate the internal resistance of the voltmeter. Again, discharge your capacitor when you are done.

Explanation / Answer

The capacitor will not be able to charge up to the maximum value provided because,

one, some of the energy supplied by the source goes in joule heating and some is used as electrostatic energy across the capacitor.

two, the source might have some internal resistance that might be added in the calculation to give a better result.

So by measuring the current and the lost voltage , internal resistance can be found out using Ohm's law.

I = V / R .

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