Capacitors

Question 1

What is capacitance?

Answer 1

Capacitance is the charge stored per unit potential difference in a capacitor.

C = Q/V given in exam

Question 2

What is a capacitor?

Answer 2

A capacitor is an electrical component that stores charge.

A parallel-plate capacitor is made of two parallel conducting plates with an insulator between them (A.K.A a dielectric).

Question 3

What is permittivity?

Answer 3

Permittivity is a measure of how difficult it is to generate an electric field in a certain material.

Question 4

What is relative permittvity?

Answer 4

Relative permittivity is the ratio of the permittivity of a material to the permittivity of free space:

εr = ε1/ε0 not given in exam

Relative permittivity is also called the dielectric constant.

Question 5

How does using dielectrics increase capacitance?

Answer 5

1. Dielectric made up of lots of polar molecules - positive end and negative end
2. Initially, molecules are pointing in a bunch of random directions
3. After charge is applied, negative ends are attracted to positive plate and vice versa - they become aligned
4. Each molecule has its own electric field, which in new alignment opposes original electric field
5. Reduces overall electric field, which reduces potential difference needed to charge capacitor - so capacitance increases

C = Q/V

Question 6

What does the time taken to charge or discharge a capacitor depend on?

Answer 6

The time taken to charge or discharge a capacitor depends on:

1. The capacitance of the capacitor - affects the amount of charge that can be transferred at a given potential difference
2. The resistance of the circuit - affects the current in the circuit

Question 7

What is the equation for the potential difference of a charging capacitor?

Answer 7

Equation for potential difference of a charging capacitor:

V = V0(1 - e^(-t/RC))

Same as charge for charging capacitor:

Q = Q0(1 - e^(-t/RC))

Question 8

What is the equation for the current of a charging capacitor?

Answer 8

Equation for the current of a charging capacitor:

I = I0e^(-t/RC)

Same as all discharging equations.

Question 9

Is the exponential graph for current against time for a charging capacitor positive or negative?

Answer 9

Current against time for a charging capacitor:

Negative

Question 10

Is the exponential graph for potential difference against time for a charging capacitor positive or negative?

Answer 10

Potential difference against time for a charging capacitor:

Positive

Question 11

Is the exponential graph for charge against time for a charging capacitor positive or negative?

Answer 11

Charge against time for a charging capacitor:

Positive

Question 12

Is the exponential graph for current against time for a discharging capacitor positive or negative?

Answer 12

Current against time for a discharging capacitor:

Negative

Question 13

Is the exponential graph for potential difference against time for a discharging capacitor positive or negative?

Answer 13

Potential difference against time for a discharging capacitor:

Negative

Question 14

Is the exponential graph for charge against time for a discharging capacitor positive or negative?

Answer 14

Charge against time for a discharging capacitor:

Negative

Question 15

What is the time constant, τ?

Answer 15

Time constant is product of resistance and capacitance.

τ = RC

1/e = 0.37
Time taken for the charge, potential difference or current of a discharging capacitor to fall to 37% of fully charged value.

(1 - 1/e) = 0.63
Time taken for the charge or potential difference of a charging capacitor to rise to 63% of fully charged value.

Question 16

How can you find the time constant from log-linear graphs?

Answer 16

Q = Q0e^(-t/RC)

ln(Q) = (-1/RC)t + ln(Q0)

Plot ln(Q) against time t, you get a straight line.

Gradient of graph is (-1/RC) and y-intercept is ln(Q0).

Question 17

What is the time to halve charge, current or potential difference of a discharging capacitor?

Answer 17

Time to halve charge, current or potential difference of a discharging capacitor:

T1/2 = 0.69RC

E.g. Find time taken for charge to halve.

Q = 1/2Q0
1/2Q0 = Q0e^(-t/RC)
1/2 = e(-t/RC)
ln(1/2) = ln(e(-t/RC))
ln(1) - ln(2) = (-t/RC)
t = 0.69RC