
Aim: to show that the Voltage across a Discharging
Capacitor decreases Exponentially with Time 
See Exponential Graphs,
Radioactive 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
microFarads (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, ΔV/Δt 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. 
