6.1 - Capacitors

Question 1

What is a capacitor?

Answer 1

An electrical component that stores charge

An insulator (sometimes 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 charge stored per unit potential difference

Measured in farads, F, or CV^-1

C = Q/V
Where:
•C = capacitance 
•Q = charge
• V = potential difference

Question 3

How is a capacitor charged?

Answer 3

• when a capacitor is connected to a DC power supply, there is a current as the power supply draws electrons from one plate and deposits them on the other plate
• this leaves one positively charged plate and one negatively charged plate
• these charges are equal and opposite due to the conservation of charge
• current will flow until the potential difference between the plates is equal to that of the emf of the power supply

Question 4

What is the purpose of a dielectric?

Answer 4

1) to stop charge from travelling across the gap between plates

2) to increase the capacitance of the device
• the dielectric polarises in the electric field, effectively increasing the charge stored on the plates
• dielectrics have an associated electrical permittivity (ability to polarise and strengthen the chat rage storage capability)
• air doesn’t polarise much and so is a poor dielectric and rarely used

Question 5

How is a capacitor discharged?

Answer 5

• when the power supply is disconnected, the electrons packed onto the negatively charged plate are no longer subject to the emf which held them in close proximity
• they repel one another and so flow round the circuit, dissipating energy
• once the charges on both plates are equal, there is no longer any potential difference, so electrons stop flowing and current drops to 0

Question 6

What is the total capacitance of capacitors in series?

Answer 6

1/C = 1/C1 + 1/C2 + 1/C3 …….

See ss 21/11/21 for derivation

Question 7

What is the total capacitance for capacitors in parallel?

Answer 7

C = C1 + C2 + C3 ……

see ss 21/11/21 for derivation

Question 8

Describe where work is done when charging a capacitor

Answer 8

• work is done by the power supply to deposit negatively charged electrons onto the negative plate as like charges repel (Coulomb’s law)
• work is done to remove electrons from positive plate as negative charges are attracted to positive regions

Question 9

What does the area under a pd-charge graph show?

Answer 9

Work done

Question 10

How do you calculate work done (capacitors)?

Answer 10

W = 1/2QV, W = 1/2 CV^2, W = Q^2 / 2C

Where:
•W = work done
• Q = charge 
• V = potential difference
•C = capacitance

Question 11

How can a capacitor be discharged?

Answer 11

• disconnecting the power supply and connecting up another electrical component
• this component is a resistor as then the resistance, and therefore the time constant, can be known to a high degree of accuracy

Question 12

What is the time constant?

Answer 12

The time taken for the voltage to discharge to 1/e (36.8%) of its initial charge

Product of circuit resistance and capacitance

𝜏 = CR

Where:
• 𝜏 = time constant
• R = total resistance in circuit
• C = capacitance

Question 13

How does resistance affect the discharge of a capacitor?

Answer 13

• the lower the resistance, the higher the current can be (Ohm’s law - current is indirectly proportional to resistance)
• if current is higher, the charge on the plates will fall to 0 faster because ∆Q = It

Question 14

How does capacitance affect the discharging of a capacitor?

Answer 14

• the larger the capacitance, the larger the charge stored per unit potential difference
• this means that more charge will need to flow before potential difference drops to 0, taking longer and increasing the time constant

Question 15

What is the equation for charging a capacitor?

Answer 15

x = x0 (1-e^-(t/CR)

Where:
• x = charge, current or potential difference
• x0 = original value of charge, current or potential difference
• t = time
• CR = capacitance x resistance (time constant)

Question 16

What is the equation for discharging a capacitor?

Answer 16

x = x0e^-(t/CR)

Where:
• x = charge, current or potential difference
• x0 = original value of charge, current or potential difference
• t = time
• CR = capacitance x resistance (time constant)

Question 17

What happens when when t = 𝜏 when discharging a capacitor?

Answer 17

The charge on the capacitor will have decreased to 37% of the original value

Due to the exponential nature of the discharging of a capacitor, this will always be true

Question 18

What are the applications of capacitors?

Answer 18

• to store & discharge large quantities of energy in a short period of time, making them useful for short pulses of energy eg camera flashes and touch screens
• uninterrupted power supplies (UPS), used as backup power supplies when mains electricity fails. UPSs are commonly found in data centres to protect hardware and in hospitals to maintain a constant power sup-ply to support machines
• converting AC to DC - once a sinusoidal AC current has passed through a wave rectifier, the current flows in one direction but magnitude varies. It can then be passed through a smoothing circuit smoother, where a capacitor stores charge when pd rises and discharges as it falls, maintaining a more constant current.