Capacitors

Question 1

Define and describe a capacitor

Answer 1

• A device designed to store charge.
• It consists of 2 conductors insulated from each other.
• When a capacitor is connected to a battery, one of the two conductors gains electrons from the battery and the other conductor loses electrons to the battery. Each plate gains an equal and opposite charge

Question 2

Describe the circuit symbol for a capacitor

Answer 2

Two parallel lines of the same length next to each other

Question 3

What is meant when it is said that the charge stored by a capacitor is Q?

Answer 3

One conductor stores charge +Q and the other conductor stores charge -Q

Question 4

Describe a circuit to measure the charge of a capacitor at a constant current

Answer 4

A variable resistor, a switch, a microammeter and a cell in series with a capacitor with a voltmeter connected across the capacitor

Question 5

Give the equation to calculate the charge of a capacitor being charged at a constant current at time t

Answer 5

Q = It

Question 6

Describe the relationship between the charge of the capacitor charged at a constant current and the pd of the source that is charging it

Answer 6

The charge Q is proportional to the pd V

The charge stored per volt is constant

Question 7

Define capacitance and give its units

Answer 7

The charge stored per unit pd
C = Q / V
Units: Farad (F) = 1 Coulomb per volt

Question 8

Explain why energy is stored in a capacitor as it is being charged

Answer 8

• When the capacitor is being charged, energy is stored in it because electrons are forced onto one of its plates and taken off the other plate.
• The energy is stored in the capacitor as electrical potential energy

Question 9

Give the equation for the energy stored by a capacitor

Answer 9

Energy stored, E = ½QV

Question 10

What happens to the energy supplied by a battery to charge a capacitor of capacitance C

Answer 10

50% of the energy supplied by the battery (=½QV) is stored in the capacitor. The other 50% is wasted due to the resistance in the circuit as it is transferred to the surroundings when the charge flows in the current

Question 11

Describe the circuit to measure the energy stored in a charged capacitor

Answer 11

By connecting a cell (with a voltmeter across it) to a capacitor in series with a switch. A joulemeter and light bulb are in parallel to the capacitor. The switch is arranged so that when one way, the capacitor charges from the cell, and when the other way, the capacitor discharges to the bulb

Question 12

How would you measure the energy stored in a charged capacitor? (do not describe the circuit)

Answer 12

The capacitor pd (V) is measured and the joulemeter reading recorded before the discharge starts. When the capacitor has discharged, the joulemeter reading is recorded again.
The difference of the 2 joulemeter readings is the energy transferred from the capacitor during the discharge process.

Question 13

What is a joulemeter used for?

Answer 13

It is used to measure the energy transfer from a charged capacitor to a light bulb when the capacitor discharges

Question 14

Explain how a thundercloud acts as a parallel charged plate

Answer 14

Because the thundercloud is charged, a strong electric field exists between the thundercloud and the ground.

Question 15

Give the potential difference between a charged thundercloud and the ground

Answer 15

V = Ed

where E is the electric field strength and d is the height of the thundercloud above the ground.

Question 16

Give the equation for the energy stored for a thundercloud carrying a constant charge Q

Answer 16

Energy stored = ½QV = ½QEd

since V = Ed

Question 17

Give the equation for the new amount of energy stored when a thundercloud is moved to a new height d’

Answer 17

Energy stored = ½QEd’

Question 18

For a thundercloud moved from height d, to a new height d’, give the equation for the increase in energy stored

Answer 18

Increase in Energy stored = ½QEd’ - ½QEd = ½QEΔd

where Δd = d’ - d

Question 19

Why is there an increase in energy stored when wind forces a thundercloud to a move further away from the ground?

Answer 19

The increase in energy stored is because work is done by the force of the wind to overcome the electrical attraction between the thundercloud and the ground and make the charged thundercloud move away from the ground

Question 20

Why does the current decrease gradually for the discharge of a capacitor through a fixed resistor?

Answer 20

Because the pd across the capacitor decreases as it loses charge
Because the resistor is connected directly to the capacitor, the resistor current (=V/R) decreases as the pd decreases

Question 21

Describe the shape of the graph of charge vs. time for the discharging of a capacitor through a fixed resistor

Answer 21

The charge decreases exponentially over time

Question 22

Give the equation for the change in charge for the discharge of a capacitor through a fixed resistor

Answer 22

Q = Q₀e⁻ᵗ/ᶜᴿ

Question 23

Give the equation for the change in potential difference for the discharge of a capacitor through a fixed resistor

Answer 23

V = V₀e⁻ᵗ/ᶜᴿ

Question 24

Derive the equation for the change in current for the discharge of a capacitor through a fixed resistor with resistance R

Answer 24

I₀ = V₀ / R
I = (V₀/R)e⁻ᵗ/ᶜᴿ
I = I₀e⁻ᵗ/ᶜᴿ

Question 25

Give the equation for the time taken for the initial charge to drop to a half its original value (the half-life)

Answer 25

t(½) = CRln2

Question 26

Define the time constant of a CR discharge circuit

Answer 26

The time taken for the charge on the capacitor to fall to 37% of its initial value
τ = CR

Question 27

Define the time constant of a CR charge circuit

Answer 27

The time take for the charge on the capacitor to reach 63% of its final charge
τ = CR

Question 28

Give 2 uses of a capacitor

Answer 28

1) Converting AC into DC

2) Time delay circuits

Question 29

Explain how a capacitor can be used with some other components to convert AC to DC

Answer 29

A diode allows the current from an AC supply to move in one direction only. This makes the current direct but ‘bumpy’ since it still has peaks where the positive current moves from the AC supply, and flat lines at 0A when current moves in a negative direction from the AC supply.
The capacitor charges as the current passes through the diode, and discharges as no current passes through the diode, which ‘smooths’ out the current round the circuit

Question 30

Give the equation for the change in current over time for the charging of a capacitor through a fixed resistor

Answer 30

Q = Qₓ(1 - e⁻ᵗ/ᶜᴿ)
where Qₓ is the final charge of the capacitor
Qₓ = Cε

Question 31

Give the equation for the change in pd over time for the charging of a capacitor through a fixed resistor

Answer 31

V = Vₓ(1 - e⁻ᵗ/ᶜᴿ)
where Vₓ is the final pd of the capacitor
but Vₓ =ε
Therefore:
V = ε(1 - e⁻ᵗ/ᶜᴿ)

Question 32

Give the equation for the change in current over time for the charging of a capacitor through a fixed resistor

Answer 32

I = (ε / R)(1 - e⁻ᵗ/ᶜᴿ)

Question 33

Describe the relationship between the change in pd and charge vs. time with the change in current vs. time for the charging of a capacitor

Answer 33

The charge Q, and potential difference V across the capacitor both rise exponentially whilst the current flow I, falls as an exponential function