Chapter 21: Capacitance

21.1 intro

explain what is happening here

1. when the capacitor is connected to the cell, electrons flow from the cell for a very short time

2. they cannot travel between the plates because of the insulation

3. the very brief current means electrons are removed from plate A of the capacitor and at the same time electrons are deposited onto the other plate B

4. plate a becomes electron deficient and plate b gains electrons

5. the current in the circuit must be the same at all points and charge must be conserved, so the 2 plates have an equal but opposite charge of magnitude Q

6. therefore, there is a pd across the plates

7. the current in the circuit falls to 0 when the pd across the plates is equal to the emf of the cell

8. the capacitor is then fully charged

9. the net charge on the capacitor plates is 0

10. the capacitor is therefore really a device that separates electrical charge into -Q and +Q

how are commercial capacitors usually marked

with their capacitance value, which indicates the amount of charge Q that the capacitor can store for a given pd V.

the capacitance of a capacitor is defined as…

the charge stored per unit pd across it. that is C=Q/V

what is capacitance measured in?

farads (F)

for any capacitor, what happens when the amount of positive and negative charged stored on the 2 plates is greater

the pd is greater

1 F = …

1 CV^-1

circuit symbol for capacitor

worked example: How many electrons?

21.2 Capacitors Intro

Rules of capacitors in parallel

capacitors in series

Together, their capacitance is less than their individual capacitances, so this combination will store less charge for a given pd. All the capacitors in series store the same charge. This is even true when they have different capacitances.

the cell is connected to the left-hand plate of the capacitor of capacitance C1 and to the right - hand plate of the capacitor of capacitance C2. these plates acquire equal and opposite charges as electrons flow from and to these plates. The middle 2 plates are not connected to the cell because of the presence of dielectric layers, but transfer of electrons between these plates ensures that they too acquire charge Q of the same magnitude. The overall charge of each capacitor is 0, but the magnitude of the charge on each plate is Q.

rules for capacitors in series

worked example: Analysing a circuit

investigating capacitor circuits

Proofs for the capacitance equations

21.3 intro - energy stored by capacitors

pushing and removing electrons - how is the movement of electrons affected by the plates of the capacitor

1. figure 2 shows an electron moving towards the negative plate of a capacitor that is being charged.

2. this electron will experience a repulsive electrostatic force from all the electrons already on the plate

3. external work has to be done to push this electron onto the negative plate

4. similarly, work is done to cause an electron to leave the positive plate of the capacitor

5. the external work is provided by the battery or power supply connected to the capacitor

6. in short, the energy stored in a capacitor comes from the energy of the battery or power supply

How can you determine the energy stored in a capacitor, using a potential difference - charge graph?

stored energy in a capacitor

energy stored in a capacitor - example

21.4 intro - discharging capacitors

Discharging a capacitor - what happens when S is opened at time t=0

what is the general relationship between pd, V, charge Q, current I, and time t?

Analysing a discharging capacitor: Worked example

Constant - ratio property of exponential decay

Time constant

Modelling exponential decay

iterative modelling

Dealing with logarithms and experimental results