Activity: Charging capacitors
This activity focuses on the energy and charged stored on capacitors. You will derive the equation for energy stored on a parallel plate capacitor and practise calculating this, apply conservation of energy when moving plates, understand the origin of the exponential nature of capacitor charging and discharging and sketch graphs of V, I and Q against t for charging and discharging.
Need to know
Consider a parallel plate capacitor charged by moving positive charges from one plate to the other as shown.
- What is the pd between the plates when uncharged?
- How much work would be required to move a very small charge from one plate to the other
As each charge is moved the PD between the plates increases
- How much work is required to move small charge ΔQ from one plate to the other in the second image?
The charging process can be represented by the V vs Q graph shown below.
We can see that the work done when charge ΔQ is added is approximately the same as the area of dark shaded rectangle. This is actually a trapezium but if ΔQ is small the approximation is good. The total work done in charging the capacitor by moving lots of small charges will be the area under the line = ½ QV.
This can also be found by integrating ∫VdQ
Substitute for V from the definition of C and show that E = Q2/2C
Exercises 75 to 77 page 265
First let's measure the pd across a capacitor as it is charged.
Set up the circuit shown
Start collecting data and connect the switch to 1 to charge C then connect to 2 to discharge.
You will need to zoom in on the different parts of the graph but you should be able to see that the charging and discharging are exponential.
- From your graph determine the time taken for the capacitor to charge so that the pd is 2/3 the final pd.
- Show that this is about the same as the time to discharge to 1/3 of the fully charged pd.
Exercises 78 and 79 page 268