Capacitors (DONE)

Question 1

What does a capacitor consist of?

Answer 1

• 2 parallel conductive plates which are separated by an air gap or insulation.

Question 2

What is a capacitor?

Answer 2

• A capacitor is a circuit component used to store electric charge.

Question 3

What is the circuit symbol for a capacitor?

Answer 3

• The circuit symbol is 2 parallel lines (plates) with a small separation space and wire emerging from both ends.

Question 4

Why are do capacitors often consist of plates wrapped around each other?

Answer 4

• In order to achieve a greater capacitance, a greater surface area is needed.
• Therefore in order to maximise surface area within a certain capacitor the plates are winded.

Question 5

How is capacitance across 2 ends of wire created in a circuit?

Answer 5

• We firstly need a cell with a positive and negative end both attached to pieces of wire.
• By considering the flow of electrons from negative to positive we can determine what charge the wires will have.
• All of the electrons on the negative end will want to repel away from each other so the electrons will spread a negative charge across the wire.
• On the positive side the electrons will be attracted to the positive end of the cell leaving the wire to be a region of positive charge.
• If you take the wire on both sides and loop it around making it longer, it gives more space for the electrons to spread out and they will repel each other as much as they can.
• The electrons in the positive end of the wire will continue to be attracted towards the positive end of the cell and leave the rest of the wire with a positive charge.
• Rather than just having 2 ends of wire pointing towards each other, you can put 2 parallel, vertical plates on the ends of the wire so we have a capacitor.
• Now when the negative charges reach the end of the wire, they are attracted towards the positive end and we then have one negatively charged plate and one positively charged plate creating a capacitor storing charge.

Question 6

What can we measure in a circuit that contains a capacitor?

Answer 6

• The 2 plates are separated by an air gap meaning it is not a complete circuit, however we can still measure the flow of current as there is a short time where the current flows until it reaches the capacitor.
• We can look at the charge Q on each of the plates, the total charge is zero as there will be an equal amount of charge and opposite charges in both plates.
• We can also look at the pd across the capacitor by attaching a voltmeter in parallel.

Question 7

How is capacitance calculated?

Answer 7

• Capacitance C = Q/V.
• Therefore it is dependant on the charge of each plate and the pd across them.
• Capacitance has the units Farad (F).

Question 8

What is capacitance?

Answer 8

• Effectively capacitance is the charge stored per unit p.d. across it.

Question 9

What is 1 Farad?

Answer 9

• 1 Farad = 1 coulomb per volt.

- A Farad is a large unit meaning we often have capacitors with a capacitance of micro farads.

Question 10

How do values of charge, p.d. and capacitance vary across capacitors in parallel?

Answer 10

• Capacitor 1 will have a certain charge Q1 stored within it, and capacitor 2 will have a charge Q2 stored within it.
• We can think of the capacitance of each capacitor with C1 and C2.
• And finally, because the capacitors are in parallel, using Kirchhoff’s second law we can say that the p.d. across each capacitor will be equal, therefore the p.d. is V.

Question 11

How can you derive an equation for the capacitance of some capacitors in parallel?

Answer 11

• Firstly, the total charge being stored is equal to the charge Q1 + Q2… therefore we can say as a rule that charge Qtotal = Q1 + Q2…
• We can then rearrange the equation C = Q/V to get Q = CV which we can substitute into the above equation leading to CVtotal = C1V + C2V…
• However due to kirchoffs second law the voltage is going to be the same for the capacitors in parallel therefore we can cancel the V’s to get the equation for capacitance in parallel:

Ctotal = C1 + C2…

Question 12

How do values of charge, p.d. and capacitance vary across capacitors in series?

Answer 12

• On capacitor 1 the charge Q1 is equal on each plate, on capacitor 2 the charge Q2 is also equal for each plate.
• The p.d. across capacitor 1 will be V1 and across capacitor 2 it will be V2.
• Kirchhoffs second law tells us that sum of pd’s = sum of emf’s therefore V1 + V2 = sum of emf’s around the circuit.
• The capacitance for each capacitor will also be C1 and C2.

Question 13

When looking at capacitors what does Q represent?

Answer 13

• Q is the charge stored on each individual plate in a capacitor.
• It is not the total charge of the capacitor which would = 0, but the charge Q will be equal and opposite for both plates in the capacitor.

Question 14

How can capacitors be connected in series within a circuit?

Answer 14

• If we had a capacitor in a circuit and increased the distance between the parallel plates it will not impact the stored charge however we could place further plates inside this gap.
• This creates 2 capacitors in series with one on the left and right hand side, for each capacitor there is a certain amount of charge on one side of the plate and the other side will have an equal and opposite charge.

Question 15

How can you derive an equation for the capacitance of capacitors in series?

Answer 15

• We know that the sum of the p.d’s is equal to the sum of the emf’s therefore Vtotal = V1 + V2…
• However using the equation C = Q/V we can rearrange to say that V = Q/C and substitute this into the equation for Vtotal.
• This means we get (Q/C)total = Q1/C1 + Q2/C2…
• If we have the same charge on both plates on capacitor 1 then it means the charge must be equal for each plate in capacitor 2 and therefore we cancel the Q’s in the equation.
• This leaves us with an equation for capacitors in series:

(1/C)total = 1/C1 + 1/C2…

Question 16

How do equations for capacitance and resistance in parallel and series circuits link?

Answer 16

• Capacitance for parallel capacitors:

Ctotal = C1 + C2…

This is opposite to resistors in parallel which is:

(1/R)total = 1/R1 + 1/R2…

• This also applies vice versa.

Question 17

Why do we use capacitors to store charge instead of just using a cell?

Answer 17

• The capacitor allows us to store a lot of energy and release it very quickly.
• This is how for example camera flashes work, they store up the energy from the battery and release it very quickly in a small amount of time creating a strong light source.

Question 18

How can we use a graph to see the energy stored in a capacitor?

Answer 18

• We can look at the energy stored by a capacitor using a graph with p.d. across the capacitor on the y axis against the charge stored on the x axis.
• When you have a greater source of emf, you have a greater pd across the capacitor and this means it stores more charge.
• The graph will show a linear relationship that if you increase the pd the charge stored will increase.
• If you have more charge stored in the capacitor it also means that it is storing more energy, the energy stored is equal to the area under the graph.

Question 19

What 3 equations can be used to find the energy stored by a capacitor?

Answer 19

• Because the energy stored is equal to the area under the pd against charge graph which is a triangle, the first equation for energy stored is:
  1. W = (½)QV.
• We also know that the capacitance C = Q/V therefore if we rearrange this to make V the subject V = Q/C.
• We can then substitute V into the equation for energy stored to get the first equation:

2. W = (½)(Q^2)/(C)
   - Finally we can rearrange the capacitance equation to say Q = CV and if we substitute this into the energy stored equation we get the final equation:
3. W = (½)CV^2
   - The 3 equations let us know how much energy is stored in a capacitor in terms of charge, pd and capacitance.

Question 20

How is an RC circuit created?

Answer 20

• You firstly need a power source such as a battery which needs to be connected up with a switch leading to a capacitor.
• The battery is going to charge up the capacitor until the pd across the capacitor = the emf.
• We can then take the switch and flick it over to another position where we create a circuit with the capacitor connected to a resistor.
• This circuit is called an RC circuit which is a resistor capacitor circuit and it is where the capacitor will discharge.

Question 21

What impacts how quickly a capacitor will discharge in an RC circuit?

Answer 21

• There are 2 things which impact how quickly the capacitor discharges.
• Firstly the size of the capacitor will impact how much charge is available and therefore the time it takes for capacitor to discharge, the size of the capacitor is directly proportional to the time it takes to discharge.
• The other factor is the resistor, the bigger the resistor the longer it takes for charge to flow through it therefore size of resistance is directly proportional to time taken to discharge.

Question 22

What is the equation for the time constant?

Answer 22

• The time constant tau, T = CR.
• Where C is capacitance and R is resistance.
• The greater the capacitor and resistance means the greater the time constant and therefore the greater the time it takes for the pd, current or charge to fall to 37% of its original value.

Question 23

How can we draw an exponential decay graph for how a capacitor discharges over a time period?

Answer 23

• An exponential decay graph has the form y = e^-x.
• On the y axis will be either charge, pd or current and along the x axis will be time.
• Using generic values X would be on the y axis.
• You can use the exponential decay graph to see how the ratio of the decrease in period 1 compares to period 2.
• You can see this by drawing lines from the time interval vertically until it reaches the graph, and then drawing a horizontal line towards the y axis from where the line and the graph meets.
• The point on the y axis where time period 1 meets the graph is X1 and so on…
• With an exponential decay graph we can say that the proportions of X1/X2 = X2/X3 = X3/X4.
• An example of where this is used is radioactive decay or in oscillations where each time something oscillates it loses 10% of its momentum.

Question 24

What equation would be used when plotting an exponential decay curve for a value of I, V or Q of a discharging capacitor?

Answer 24

• X = X0*e^-[(t)/(CR)].
• Where X is the new value, X0 is the original value, e is an irrational number on calculator, t is the time period elapsed and CR is the time constant.
• X could be quantities of I, V or Q.
• This means if we want to know the current after a certain amount of time we can say that the current flowing I = Io* e^-[(t)/(CR)].
• The value of CR = the time constant tau, and effectively it means there is a unit of time divided by a unit of time in the formula which results in a dimensionless quantity.
• This would equation allow us to plot the exponential decay of the current, pd or charge of a discharging capacitor.

Question 25

What is the time constant, tau?

Answer 25

• The time constant tau for a discharging capacitor is equal to the time taken for the pd to fall to 37% of its initial value.
• It is 37% because when the time constant is equal to the time t it is effectively e^-1, and if you work out e^-1 then the value is around 0.37, so when you have 37% of the original value that is equal to the time constant.

Question 26

How does a capacitor gain charge in a circuit?

Answer 26

• Firstly a very simple circuit with a cell a capacitor and a switch is needed to charge the capacitor.
• Once the switch closes there will be a flow of electrons coming from the negative end of the terminal trying to get to the positive end.
• As more electrons aim to reach the positive terminal there is going to be a build up of negative charges on the first plate of the capacitor, and an equal and opposite charge on the second plate.

Question 27

What happens to current as a capacitor is being charged in a simple circuit?

Answer 27

• As the first plate of the capacitor gains a negative charge, there is going to be less need for the electrons to get to the negatively charged plate.
• We find that the current has an exponential decrease, this means that as time goes on the amount of current in the circuit decreases.
• Therefore we can say at any point the current I = Io* e^-[(t)/(CR)].

Question 28

How does charge on the capacitor change as it is being charged in a simple circuit?

Answer 28

• As time goes on the amount of charge builds up, meaning on a graph we get a line similar to the first half of an x^2 graph.

Question 29

How does pd across the capacitor change as it is being charged in a simple circuit?

Answer 29

• Considering that the cell will have a pd across it of V0 and the capacitor will have a pd of Vc we can make an equation to find Vc..
• The equation to find the pd across the capacitor Vc = V0(1 - e^-[(t)/(CR)].
• This creates a graph which is a mirror to the exponential decay current graph.
• This means when Vc is 1, current will be near 0 and when current is 1, Vc will be near 0.
• As time t gets bigger the value of Vc will get smaller meaning Vc tends towards V0 over time.

Question 30

how are capacitors used in circuits with alternating currents?

Answer 30

• Capacitors can be used in circuits to change an alternating current to a direct current.
• We can turn the ac to dc by firstly introducing a diode which only allows current to flow in one direction.
• On a graph we can see that there will be periods of 0 current where the current in one direction is blocked meaning it is not a very good power supply.
• We need a more constant power supply so we add a capacitor which is charged by the current which does pass through the diode.
• But rather than the current decreasing rapidly the capacitor can discharge the current at a slower rate until the circuit is charged up again.
• This smoothes the power supply by using the diode and capacitor in series.

Question 31

How can capacitors be used for camera flashes and fusion reactors?

Answer 31

• Capacitors can be used when we need to generate a lot of power in a short amount of time.
• For a camera the battery will charge up the capacitor over a period of seconds.
• The capacitor will then release that energy in a short amount of time during the flash.
• This causes a high power output due to the equation E = p/t.
• This is also useful in fusion reactors where we can charge up a bank of capacitors over many minutes and then release the energy in a small amount of time creating a Tera Watts of power which is needed to allow fusion to occur.

Question 32

How can capacitors be used as a short term power store in electrical devices?

Answer 32

• Capacitors can be used as a power supply for a short amount of time in electrical devices.
• There will be lots of capacitors in the device so if the ac supply powering the device is interrupted, there’s just enough energy to stop the device turning off completely.