1. Potential Difference and Capacitance
Chapter 20

2. Fact: The Work done in bringing a Charge from one point to another in an electric field does not depend on the path taken.

3. The amount of work that must be done to bring a charge of one coulomb from B to A is called the Potential Difference between B and A.

4. What is Potential Difference?
The Potential Difference between two points in an electric field is the work done in bringing a charge of +1 coulomb from one point to the other.

5. Define the volt. What is the SI Unit of Potential Difference?
The SI Unit of potential difference is the volt (V).
Define the volt.
One volt is one joule per coulomb
i.e V = 1 J C-1.

6. A charge of 4 coulombs passes through a potential difference of 10 volts. How much work is done?
10 volts means 10 joules of work are done for each coulomb transferred.
Total work done
= Work done per coulomb × Number of coulombs transferred
= (10) × (4) = 40 joules

7. W joules of work are done.
A charge of Q coulombs
moves through a Potential Difference of V volts.
W joules of work are done.
What formula relates Q, V and W ?
Work Done = Charge Transferred × Voltage

8. A Battery and its circuit symbol
A battery has two terminals. The negative terminal has an excess of negative charge and the positive one has an excess of positive charge.
There is thus an Electric Field in the space between the terminals. The higher the voltage of the battery the stronger this electric field is.

9. What is an Electric Current?
An Electric Current is a flow of electric charge.

10. What is meant by Potential at a Point?
The potential difference between a point and the Earth is called the potential of that point.

11. Work must be done to bring a positive charge from the ground up to the charged conductor.
This is because the positive charge is repelled by the positive charge on the conductor as it gets near it.

12. As charge is added to the conductor the potential difference between it and the ground increases. Thus its Potential Increases.
FACT: The charge on the conductor and its potential are directly proportional to each other.

13. As you add positive charge to a conductor its potential increases.
Different conductors reach different potentials even if they carry the same amount of charge.
The potential reached depends on the shape and size of a conductor.
The potential reached is directly proportional to the charge on the conductor.
i.e Q  V Q = C V, where C is a constant
C is called the Capacitance of the Conductor.
The bigger C, the more charge the conductor can hold for a given potential.

14. What is Capacitance?
The Capacitance of a conductor is the ratio of the charge on the conductor to its potential.
Where C is the Capacitance of the conductor
Q is the Charge on the conductor
V is the Potential of the conductor

15. What is the SI Unit of Capacitance?
The SI Unit of Capacitance is the farad (F).
A conductor has a capacitance of 1 farad if placing a charge if 1 C on it raises its potential by 1 volt,
i.e., 1 farad = 1 coulomb per volt ( C V-1 ).

16. The farad is a very large unit.
In practice we use the microfarad, the nanofarad and the picofarad where:
1 microfarad = 1 F = F
1 nanofarad = 1 nF = F
1 picofarad = 1 pF = F

18. The capacitance of a charged conductor is increased by bringing an oppositely charged conductor or an earthed conductor near it.

19. The capacitance of a charged conductor is increased by bringing an oppositely charged conductor or an earthed conductor near it.

20. What is a Parallel Plate Capacitor?
A Parallel Plate Capacitor is two identical parallel conducting plates separated by an insulator (called a Dielectric).
Conducting Plate
Insulator

21. The Capacitance of a Parallel Plate Capacitor is given by:
Where: C is the Capacitance
A is the Area of Overlap of the plates
d is the Distance between the plates
ε is the Permittivity of the dielectric

22. Area of Overlap of Plates

23. To show that a Charged Capacitor Stores Energy
Use the equipment shown.
Charge the capacitor by connecting the battery across it.
Remove the battery and connect a bulb across the capacitor.
The bulb will flash as the capacitor discharges, showing that it stores energy.

24. The Energy Stored in a Charged Capacitor
is given by:
Where: W is the Energy Stored
C is the Capacitance
V is the Potential Difference between the plates

25. Thus a Charged Capacitor Blocks d.c.
If the circuit below is set up and the switch closed, current flows for a short while and the capacitor charges up.
When the capacitor is charged no more current flows.
Thus a Charged Capacitor Blocks d.c.

26. If the circuit below is set up alternating current will flow.
This is because as the a.c. changes direction the capacitor continually charges and discharges.
The greater the capacitance of the capacitor the less opposition it offers to a.c..

27. A Capacitor Conducts a.c. but not d.c.
A charged Capacitor blocks d.c.
A Capacitor conducts a.c. since it charges and discharges as the a.c. changes direction.