Capacitors

Question 1

Define Capacitance

Answer 1

The charge stored, per unit Volt, across the plates of the capacitor [F]

Question 2

What do the gradient and area under this graph represent?

Answer 2

Gradient → Capacitance

Area → Work done (Energy Stored)

Question 3

What is wrong with this?

Answer 3

C = capacitance → not the charge!!!

Question 4

When building a capacitor how do you maximize the capacitance?

Answer 4

1. Increase the area for which the plates overlap
2. Decrease the plate separation
3. Place dielectric between plates

Question 5

What does it mean if the relative permittivity of a dielectric (ε_r) is 5.0?

Answer 5

The capacitor stores 5x more charge with the dielectric between the plates!

Question 6

How does adding a dielectric increase the capacitance of a capacitor?

Answer 6

1. Dielectric contains polarised molecules
2. They align with the field between the plates
3. Initially the charges on each plate cancels out (counter electric field) with the dielectric reducing the voltage between the plates charge remains the same
4. Due too the lower voltage across the plates the capacitor starts to charge again until the voltage across the plates equals the battery’s voltage
5. The capacitor now has a greater charge across it
6. And V is the same as before so capacitance has increased from C=Q/V

Question 7

What happens if the dielectric is removed?

(Capacitor still connected to battery)

Answer 7

1. Polarised molecules removed
2. Some electrons leave negative plate
3. Attracts more electrons to positive plate
4. Q has decreased but V same
5. C decreases (C=Q/V)

Question 8

What happens if the dielectric is removed?

(When the Capacitor is disconnected from battery)

Answer 8

1. Polarised molecules removed
2. But charge is trapped on plates as no current is flowing
3. Same Q but with lower C (because no dielectric so no counter electric field)
4. V increases (V=Q/C)

Question 9

How does this capacitor charge?

(When switch 1 is closed)

Answer 9

1. Electrons flow from the negative terminal of the battery
2. To the connected parallel plate (right plate)
3. Electrons are repelled from the opposite plate (left)
4. And attracted to the positive terminal of the battery
5. Charge across Parallel plates

Question 10

How does this capacitor discharge?

(When switch 2 is closed)

Answer 10

1. Electrons flow from the negative plate (right)
2. Through the resistor
3. To the other plate (left)
4. Decreasing charge difference across plates

Question 11

What are the capacitor charging equations?

Answer 11

Q = Q₀(1-e^-t/RC) Q₀ = final charge

V = V₀(1-e^-t/RC) V₀ = final voltage

I = I₀(1-e^-t/RC) I₀ = inital current

Question 12

What are the capacitor discharging equations?

Answer 12

Q = Q₀e^-t/RC Q₀ = initial charge

V = V₀e^-t/RC V₀ = initial voltage

I = I₀e^-t/RC I₀ = initial charge

Question 13

What is the time constant?

Answer 13

The time taken for the charge to fall to 37% of its original value (1/e)

Calculated by resistance * capacitance

Question 14

What is given by the gradient and y-intercept of a discharging/charging capacitor’s charge - time graph?

Answer 14

Gradient - Current at a point

Y-intercept - Initial charge

Question 15

What is given by the y-intercept of a discharging/charging capacitor’s P.D - time graph?

Answer 15

Initial P.D

Question 16

What is given by the area under the graph and the y-intercept of a discharging/charging capacitor’s current - time graph?

Answer 16

Area under curve - Charge released/gained between points

Y-intercept - Initial current

Question 17

How is the time constant for a charging capacitor expressed?

Answer 17

1 - 1/e (or 63% of max charge).

For the second time constant, the charge will increase by 63% of the remaining 37%, and so on.

Question 18

Will a charging capacitor ever reach maximum charge?

Answer 18

No.

The charging curve will asymptote with Q₀

Question 19

Will a discharging capacitor ever reach 0 charge?

Answer 19

No.

The discharging curve will asymptote with the x-axis

Question 20

After how long can it be said that a discharging capacitor is effectively discharged / charging capacitor has effectively charged?

Answer 20

5 time constants

Question 21

Explain the half-lives for a charging capacitor

Answer 21

1 half-life : time taken to reach 50% of charge

2 half-lives : time taken to reach 75% of charge (50% of remaining 50% + original)

3 half-lives : time taken to reach 87.5% of charge (50% of remaining 25% + original etc.

Question 22

How can you find the time constant from a graph of half-lives?

Answer 22

• Find x & y values for each half-life (x values being time)
• Find the mean of these values of time (values being length of each half-life)
• ln|0.5|= t_½/RC with ln|0.5|representing half of max charge
• Sub mean t_½ value into formula and solve

Question 23

How does adding a dielectric to a capacitor affect discharge?

Answer 23

The capacitor will discharge faster with a dielectric

Question 24

What does the equation ε_r = c/c₀ mean?

Answer 24

ε_r - Dielectric constant

c - capacitance with a dielectric

c₀ - capacitance without dielectric

Question 25

Describe the change in voltage across a capacitor and voltage across a resistor as the capacitor is charged

Answer 25

• The voltage across the resistor will decrease exponentially
• The voltage across the capacitor will increase exponentially

Question 26

If during discharging, the current follows an exponential decrease graph, how can we achieve constant current discharge?

Answer 26

Through the use of a variable resistor, we can increase resistance while the voltage is decreasing to keep the current at a steadily decreasing power

Question 27

How is relative permittivity calculated?

Answer 27

The ratio of the capacitance with the dielectric to the capacitance without the dielectric
( C / C₀ )