Capacitors

Question 1

what is a capcitor

Answer 1

• is an electrical component that stores charge on 2 separate metallic plates
• an insulator, called a dielectric, is placed between the plates to prevent the charge from travelling across the gap

Question 2

what is capacitance

Answer 2

the capacitance, C, is the charge stored, Q, per unit potential difference, V, across the two plates. Therefore we have C = Q/V. It is measured in Farads, F (1F = 1CV^-1)

Question 3

what is the equation for the total capacitance in series?

Answer 3

1/C total = 1/C1 + 1/C2 + …

Question 4

what is the equation for the total capacitance in parallel

Answer 4

C total = C1 + C2 + …

Question 5

what does the area under the graph of charge against pd represent

Answer 5

The energy stored by the capacitor

Question 6

describe the Q against t graph for the discharging of a capacitor through a resistor

Answer 6

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Question 7

describe the V against t graph for the discharging of a capacitor through a resistor

Answer 7

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Question 8

describe the I against t graph for the discharging of a capacitor through a resistor

Answer 8

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Question 9

describe the Q against t graph for the fixed charging of a capacitor through a resistor

Answer 9

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Question 10

describe the V against t graph for the charging of a capacitor through a resistor

Answer 10

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Question 11

what is a time constant?

Answer 11

the time it takes for the charge in a capacitor falls to 37% of the initial value given by RC (resistance x capacitance).

A capacitor is considered fully discharged after 5-time constants

Question 12

How was 37% derived when using the time constant?

Answer 12

• Start with the formula Q = Q0 e^-t/RC
• when t = RC (after 1 time constant), the formula becomes Q = Q0 e^-1
• e^-1 ≈ 0.37, which is where 37% came from

Question 13

what is the half time of a capacitor?

Answer 13

T1/2 = ln(1/2)RC

Question 14

what equations do we require for charging a capacitor

Answer 14

charging up a capacitor produces

Q = Q0(1 - e^-t/RC) & V = V0(1 - e^-t/RC) where V0 is the battery PD and Q0 = CV0

Question 15

how does a capacitor charge up

Answer 15

1. electrons move from negative to positive around the circuit
2. the electrons are 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 build up on plate A and an equal amount of electrons are removed from plate B, creating a potential difference across the plates
5. when the p.d across plates = source p.d, the capacitor is fully charged and current stops flowing

Question 16

describe and explain in terms of the movement of electrons how the p.d across a capacitor changes, when it discharges across a resistor

Answer 16

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

Question 17

State some uses of capacitors

Answer 17

• flash photography
• nuclear fusion
• backup power supplies
  also
• DC blocking
• Smoothing AC to DC
• Tuning (Resonating magnetic field)

Question 18

state the 3 expressions for the energy stored by a capcitor

Answer 18

E = 1/2 (Q^2/C) = 1/2 (QV) = 1/2 (CV^2)

Question 19

what 2 factors affect the time taken for a capacitor to charge or discharge

Answer 19

• the capacitance of the capacitor, C. This affects the amount of charge that can be stored by the capacitors at any given potential difference across it
• The resistance of the circuit, R. This affects the current in the circuit and how quickly it flows, hence how quickly the capacitor charges/discharges

Question 20

What is Kirchhoff’s first law

Answer 20

The sum of currents into a point equals sum of current out of that point
- Charge is conserved