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Electricity and Magnetism
 
Aim: to show that the Voltage across a Discharging Capacitor decreases Exponentially with Time
See Exponential Graphs, Radio-active Decay
 
A capacitor is a device used to store electric charge.
The capacitance of a capacitor is a measure of the quantity of charge, Q, it can store for a given potential difference, V.
Capacitance is defined by the following equation:
and so the units of capacitance are CV-1 and 1 CV-1 is called 1Farad (1F).
 
Method
Because the Coulomb is a very large quantity of charge, the capacitors you will be working with will probably have a capacitance in the region of micro-Farads (μF); something like 1000μF will be convenient for this experiment.
Some preliminary tests will be needed to find a suitable value for the resistance R in order to have a reasonable discharge rate.
For a 1000μF capacitor try values of R around 10kΩ
Plot a graph of V against t.
 
Charge the capacitor by closing the switch.
Note the reading of the voltmeter; this is the voltage at t = 0.
Open switch and start your timer (simultaneously).
Measure the time taken for the voltage to fall to, say, 5V.
Recharge the capacitor and measure the time for the voltage to fall to some other figure, say, 4.5V.
Repeat for other voltages.
 
To prove that the curve is exponential, there are various possibilities:
 
1. If the graph is exponential, it will be found that the rate of fall of voltage is directly proportional to voltage.
  Therefore we can write
 
  Now, ΔVt is the slope of the graph, so if we measure the slope at different voltages, we can see if the graph is exponential.
   
2. Another way to prove that the results show an exponential fall in voltage is to find the time taken for the voltage to fall to a given fraction (usually half) of its starting value.
  If the graph is exponential, the "halving time" should be constant no matter what time you consider as the start.
 
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