Capacitors

Question 1

Define capacitance (words and equation)

Answer 1

The charge per unit potential difference stored by a capacitor.

C = Q/V

Question 2

Explain dielectric action

Answer 2

• Dielectric made up of polar molecules - when there is no electric field the direction of they point in is random.
• When a charge builds up on the plates of the capcitor, an electric field is applied across the dielectric.
• Molecules line rotate to align their electric fields in the opposite direction to the applied field, reducing the overall electric field and therefore the p.d. needed to charge the capacitor, so the capacitance increases,

Question 3

What is relative permittivity?

Answer 3

The ratio of permittivity of a material to the permittivity of free space.

Question 4

How is capacitance related to relative permittivity (formula)?

Answer 4

C = Aε₀ε_r/d

Where:

A = area of each plate (not total area of both plates) in m²

ε₀ = permittivity of free space

ε_r = relative permittivity of dielectric

d = separation of the plates in m

Question 5

What does the graph of Q against V look like and what can it tell us?

Answer 5

• Straight line through origin w/ positive gradient
• Area underneath is energy stored by capacitor
• Gradient is capacitance

Question 6

Draw the charging graphs for current, p.d. and Q against t.

Answer 6

Question 7

Draw the discharging graphs for current, p.d. and Q against t.

Answer 7

Question 8

Draw the circuit to test capacitor charging and discharging.

Answer 8

As in picture but w/ a resistor on the cell loop as well

Question 9

Describe how a capacitor charges.

Answer 9

• Switch closes, currents start to flow.
• Electrons flow onto plate connected to -ve terminal of cell, so a -ve charge builds up. This repels electrons off the other plate, giving it an equal and opposite (+ve) charge.
• A p.d. forms between the two plates.
• As charge builds up, electrostatic repulsion increases which limits the number of electrons that can be deposited.
• When p.d. across capacitor is same as across cell, current stops flowing.

Question 10

What is the formula for current when:

• charging?
• discharging?

Answer 10

Both the same:

I = I₀e^-t/RC

Where:

• I* = current at time t
• I*₀ = the maximum (initial) current

Question 11

What are Q₀ and V₀ in the formulae for charge and p.d. when charging and discharging a capacitor?

Answer 11

The maximum charge that can be stored and maximum (cell) p.d.

Question 12

What is the time constant of a capacitor?

Answer 12

τ = RC is the time taken for the charge, p.d. or current to fall to 37% its value when fully charged, or time taken for charge or p.d. across a capacitor to increase to 63% its value when fully charged.

Question 13

How many time constants must pass before a capacitor is essentially fully discharged?

Answer 13

5RC

Question 14

How can you determine the time constant graphically?

Answer 14

• Plot the logarithmic form of any of the charging equations e.g. ln(Q) = (-1/RC)t + ln(Q₀).
• Gradient is -1/RC, so divide -1 by gradient to get time constant.

Question 15

How long does it take for the current, p.d. or charge to halve from a discharging capacitor (in terms of time constants)?

Answer 15

0.69RC