Capacitance

Question 1

What is a capacitor?

Answer 1

A capacitor is an electrical component that can store electrical charge.

Question 2

How is a capacitor made

Answer 2

Capacitors are made up of two conducting plates separated by a gap or a dielectric (an insulating material).

Question 3

What is a capacitor circuit symbol?

Answer 3

See CGP Pg 140

Question 4

How does a potential difference occur in a capacitor

Answer 4

When a capacitor is connected to a power source, positive and negative charge build up on opposite plates. The insulating material (which could be an air gap) stops charge moving between the two plates, so a potential difference is created.

Question 5

What can be said about the type of field created

Answer 5

This creates a uniform electric field This creates a uniform electric field

Question 6

How the capacitance be calculated

Answer 6

C=Q/V

Q is the charge in coulombs
V is the potential difference in volts
C is the capacitance in farads

Question 7

How can the total capacitance in a parallel circuit be calculated

Answer 7

If you put two or more capacitors in a parallel circuit, the potential difference across each one is the same.
Each capacitor can store the same amount of charge as it would if it was the only component in the circuit.
So, the total capacitance is just the sum of the individual capacitances:

C(total) = C(1) + C(2)

Question 8

How can the total capacitance in a series circuit be calculated

Answer 8

When you put capacitors in a series circuit, the potential difference is shared between them.
Each capacitor stores the same charge.
It can be shown that:

1/C(total) = 1/C(1) + 1/C(2)

Question 9

How can you investigate capacitors in series and in parallel

Answer 9

See CGP pg 141

Question 10

Imagine an electron moving towards the negative plate of a capacitor that is being charged.
Hence, Explain how a capacitor is charged by the battery

Answer 10

This electron will experience a repulsive electrostatic force from all the electrons already on the plate. External work has to be done to push this electron onto the negative plate. Similarly, work is done to cause an electron to leave the positive plate of the capacitor. The external work is provided by the battery or power supply connected to the capacitor. In short, the energy stored in a capacitor comes from the energy of the battery or power supply.

The electrical energy produce by the battery can be calculated by charge x potential difference

Question 11

How can the equation w=1/2 QV be derived

Answer 11

The energy stored by a capacitor is equal to the work done to deposit the charge on the plate. So, you can find the energy stored from the area under a graph of p.d. against charge stored on the capacitor.
The p.d. across the capacitor is proportional to the charge stored on it, so the graph will be a straight line through the origin. The energy stored is given by the yellow triangle.

Question 12

What are three expression for energy stored by a capacitor that can be determined from w=1/2 QV

Answer 12

W=1/2 v^2C

W=1/2QV

W=Q^2/2C

Question 13

What are uses of capacitors

Answer 13

Flash photography — when you take a picture, the capacitor has to discharge really quickly to give a short pulse of high current to create a brief, bright flash.
2) Back-up power supplies — these often use lots of large capacitors that can release charge for a short period if the power supply goes off — e.g. for keeping computer systems running if there’s a brief power outage.
Smoothing out p.d. — when converting an a.c. power supply to d.c. power, capacitors charge up during the peaks and discharge during the troughs, helping to maintain a constant output.

Question 14

What is special about how capacitors release stored energy

Answer 14

They can discharge quicker than batteries, which makes them very useful.

The amount of charge that can be stored and the rate at which it’s released can be controlled by the capacitor chosen.

Question 15

How do you get a capacitor fully charged and record the current, Pd and R as you do so?

Answer 15

1) Set up the test circuit shown in the circuit diagram. See pg 143

1) Close the switch to connect the uncharged capacitor to the power supply.
Let the capacitor charge whilst the data logger records both the potential difference (from the voltmeter) and the current (from the ammeter) over time.

When the current through the ammeter is zero, the capacitor is fully charged.
You can then use a computer to plot a graph of charge, p.d. or current against time.

Question 16

What do the graphs of a charging capacitor look like?

Explain these graphs in terms of electron flow

Answer 16

See 143 pg

As soon as the switch closes, current starts to flow. The electrons flow onto the plate connected to the negative terminal of the power supply, so a negative charge builds up.

This build-up of negative charge repels electrons off the plate connected to the positive terminal of the power supply, making that plate positive. These electrons are attracted to the positive terminal of the power supply.

An equal but opposite charge builds up on each plate, causing a potential difference between the plates. Remember that no charge can flow between the plates because they’re separated by an insulator (gap or dielectric).

Initially the current through the circuit is high. But, as charge builds up on the plates, electrostatic repulsion makes it harder and harder for more electrons to be deposited. When the p.d. across the capacitor is equal to the p.d. across the power supply, the current falls to zero. The capacitor is fully charged.

Question 17

How do you fully discharge a capacitor

Answer 17

Disconnect the power supply from the test circuit above, reconnect the circuit and close the switch.
Let the capacitor discharge whilst the data logger records potential difference and current over time.
When the current through the ammeter and the potential difference across the plates fall to zero, the capacitor is fully discharged.

Question 18

Plot graphs of I, V and R for a discharging capacitor and explain

Answer 18

See CGP pg 143

The electrons (current) flow from the negative plate to the positive plate (shown above).
Initially, the current is high, but as the charge leaves the plates, the potential difference across the plates decreases. So the electrostatic repulsion decreases, reducing the flow of current.

Question 19

How can you predict how stored charge will change over time for a discharging capacitor using an equation

Answer 19

for any discharging capacitor with capacitance C and initial charge Q, in a circuit with resistance R. You need to find the change in charge over a tiny time interval and repeat this process for a long period of time. To do this, you’ll need an equation which relates Δ Q and Δ t.

In terms of equations

I= ΔQ/Δt and I= V/R

So ΔQ/Δt = V/R

You also know for capacitors Q=CV and V=Q/C

Therefore ΔQ/Δt=-Q/RC

= ΔQ=-Q Δt/RC

Question 20

How could you use spreed sheet modeling to draw a graph of charge against time for a discharging capacitor

Answer 20

See CGP page 144

Question 21

What can be said about the rate at which charge on a discharge capacitor decrease

Answer 21

It’s decreases exponentially

Question 22

What is the formula left for the charge/ voltage/ current on a discharging capacitor?

Answer 22

x=x₀e^(-t/CR)

I=I₀e^(-t/CR) Q=Q₀e^(-t/CR) V=V₀e^(-t/CR)

Where X₀ is the value when the capacitor is fully charged
t is the time since discharging began
R is the resistance
C is capacitance (F)

Question 23

How do you calculate the charge, Pd and current for a charging capacitor

Answer 23

x=x₀(1- e^(-t/CR) )

I=I₀e^(-t/CR)) Q=Q₀(1 - e^(-t/CR)) V=V₀(1 - e^(-t/CR))

Notice the charging current decrease exponentially

Where X₀ is the value when the capacitor is fully charged
t is the time since discharging began
R is the resistance
C is capacitance (F)

Question 24

What does the time it takes to charge up a capacitor depend on?

Answer 24

1) The capacitance of the capacitor (C). This affects the amount of charge that can be transferred at a given voltage.
2) The resistance of the circuit (R). This affects the current in the circuit.

Question 25

What equation is an expression for the time constant

Answer 25

τ=CR

Question 26

What facts can be ascertained from the time constant expression

Answer 26

T, the time constant, is the time taken for the charge, potential difference or current on a discharging capacitor to fall to 37% of its initial value.
It’s also the time taken for the charge or potential difference of a charging capacitor to rise to 63% of it’s maximum value.
The larger the resistor in series with the capacitor, the longer it takes to charge or discharge.

Question 27

What is the time taken for the capacitor to fully charge or discharge, in terms of CR

Answer 27

5CR

Question 28

How can you CR for a discharging capacitor using a graph?

Answer 28

To find CR, you can plot a graph of InQ against t while discharging (p.d. or current would work too). The gradient of the line gives you -1/CR

Question 29

How can the time constant be found experimentally

Answer 29

T can be found experimentally by using a voltmeter and timing how long it takes a discharging capacitor to reach 37% of its starting potential difference.