Chapter 21: Capacitors

Question 1

capacitor

Answer 1

• electrical component that stores charge on separate metallic plates
• insulator, dielectric, between plates to prevent charge from travelling across the gap

Question 2

Capacitance

Answer 2

charge stored per unit potential difference across the two plates

Question 3

Relative permittivity

Answer 3

• Ratio of charge stored with dielectric between two plates to charge stored without it
• greater relative permittivity, greater capacitance of capacitor

Question 4

How to you add capacitors in series?

Answer 4

1/Ct = 1/C1 + 1/C2…

Question 5

How do you add capacitors in parralel

Answer 5

Ct = C1 +C2 +…

Question 6

What does the area under a charge against pd graph represent?

Answer 6

energy stored by the capacitor

Question 7

Time constant

Answer 7

time taken for the charge of a capacitor to fall to 37% of the initial value, given by RC

Question 8

How do capacitors charge up?

Answer 8

1) Electrons move from negative to positive around circuit
2) Electrons deposited on plate A, making it negatively charged
3) Electrons travel from plate B to the positive terminal of the battery, giving the plate a positive charge
4) Electrons deposited on plate A and an equal amount of electrons are removed from plate B, creating a potential difference across the plates
5) When the pd across the plates = source pd, the capacitor is fully charged and the current stops flowing

Question 9

How does the PD across a capacitor change when discharging. Describe in terms of electron movement.

Answer 9

1) Electrons move in the opposite direction than when the capacitor was charging
2) Charge on one plate A decreases as it loses electrons, and plate B gains electrons, neutralising them
3) PD decreases exponentially across the plates

Question 10

Uses of Capacitors

Answer 10

• flash photography
• nuclear fusion
• backup power supply
• smoothing AC to DC
  STORAGE OF ENERGY

Question 11

Energy equation for Capacitor

Answer 11

E = 1/2 Q V

Question 12

What factors affect the time taken to discharge/charge a capacitor?

Answer 12

• Capacitance, affects the amount of charge that can be stored by the capacitors at any given potential difference
• Resistance, affects the current in the circuit and how quickly it flows, hence how fast it charges/discharges

Question 13

Techniques and Procedures used to investigate capacitors in both series and parallel combinations using ammeters and voltmeters

Answer 13

Part 1 (Single Capacitor): Charge at constant current, record current, voltage, and time. Plot Q against V gradient = capacitance.

Part 2 (Parallel Capacitors): Repeat with 2 capacitors in parallel. Combined capacitance = sum of individual capacitances.

Part 3 (Series Capacitors): Repeat with 2 capacitors in series. Combined capacitance = 1/C = 1/C1 + 1/C2
Key Formula: Q = I x t

Question 14

Formula for Capacitance and units

Answer 14

C = Q/V, units FARAD

Question 15

Techniques and procedures to investigate the charging of a capacitor using both meters and data loggers

Answer 15

Method:
1. Set up the circuit.
2. Close the switch, record voltage and current at t = 0 and every 5 seconds until ~120s.
3. Repeat twice more, recording voltage and current each time.

Graphs & Calculations:
- Calculate mean voltage and current for each time.
- Plot:
- Voltage vs Time (Exponential growth: ( V = V_0(1 - e^{-t/RC}) )).
- Current vs Time (Exponential decay: ( I = I_0e^{-t/RC} )).
- Area under I-t graph = Charge stored.

Question 16

Techniques and procedures to investigate the discharging of a capacitor using both meters and data loggers

Answer 16

Method:
1. Set up apparatus as shown.
2. Switch to position A to fully charge the capacitor.
3. Switch to position B, start the stopwatch, and record ( V ) at ( t = 0 ) and every 5s until ~120s.
4. Repeat twice, calculate average V for each t.
5. (Optional: Repeat with different resistors/capacitors to study time constant variation).

Graphs & Calculations:
- Calculate ( \ln(V) ) for each ( t ).
- Plot ( \ln(V) ) vs ( t ): straight line, gradient = ( -1/RC ).

Question 17

How does Q I and V change as a capacitor charges?

Answer 17

V and Q exponentially increase
I exponentially decrease

Question 18

How does Q I and V change as a capacitor discharges?

Answer 18

Q I and V exponentially decreases