Chapter 21 - Capacitance

Question 1

Define Capacitor

Answer 1

A capacitor is an electrical component that stores charge on two separated metallic plate, with a dielectric (insulator) between them. Which prevents charge from travelling between them.

Question 2

Define Capacitance

Answer 2

Capacitance is defined as the charge stored per unit of potential difference.
C = Q/V
Capacitance is measured in Farads (CV⁻¹).

Question 3

What happens when a Capacitor is connected to a DC power supply?

Answer 3

· Brief current as the power supply draws electrons from one plate and transfers them to the other.
· This leaves a +ve and -ve plate, charges are equal and opposite.
· Current will flow until the potential difference between the plates is equal to the e.m.f.

Question 4

Capacitors in Series

Answer 4

Cₜ⁻¹ = C₁⁻¹ + C₂⁻¹ + …..
This is derived from Kirchhoff’s Second Law

Question 5

Capacitors in Parallel

Answer 5

Cₜ = C₁ + C₂ + …..
This is derived from Kirchhoff’s First Law

Question 6

Work Done in Capacitors

Answer 6

Work must be done to pull electrons from the positive plate and deposit them on the negatively charged plate.
This work is equivalent to the area under a Voltage Charge graph.
W = ½QV

Question 7

Uses of Capacitors

Answer 7

· Camera Flashes
· UPSs (Uninterrupted Power Supplies)
· AC to DC converters, as they smooth the curves created by AC.

Question 8

Discharging Capacitors

Answer 8

· When the power supply is disconnected, there is no emf holding the electrons to the negative plate, so they repel each other and force themselves around the circuit.
· This repulsion decreases as more electrons are dissipated, therefore dissipating exponentially.
· x = x₀e^-(t/CR) where x can be current, charge or voltage.

Question 9

What is the time constant for capacitors?

Answer 9

The time constant (τ) is equivalent to Capacitance x Resistance (τ=CR). It is the time taken for a capacitor to discharge to 37% of its original value.

Question 10

Charging Capacitors

Answer 10

· Repulsion increases as more electrons build up on the negative plate.
· Capacitors charge exponentially as well.
· X = X₀(1-e^-(t/CR))

Question 11

Investigating Capacitance

Answer 11

· Set up circuit with DC power supply, a capacitor, a resistor and ammeter in series, a voltmeter in parallel over the capacitor.
· Take readings of voltage and current taken at intervals shorter than the time constant.
· Plot a graph of current or voltage against time.
· Look for the value with is 37% of the original value and divide this time by the resistance to get capacitance.

Question 12

Relationship between Capacitance, area of plates and distance between plates.

Answer 12

C = ε₀A/d