PHYSICS A2 UNIT 4 SECTION 3: CAPACITANCE

CAPACITORS / ENERGY STORED BY CAPACITORS / CHARGING AND DISCHARGING

# Question CAPACITORS

1 What is current? • Current is the rate of flow of charge in a circuit • Is equal to current x time 2 What is an electric current in a metal conductor? • An electric current in a metallic conductor is a flow of ‘free’ electrons due to a pd across the

ends of the conductor 3 What is the potential difference between two points? • The potential difference (p.d) between two points is the work done per unit charge to move a

charged object from one point to another 4 What is the equation for power? • P=IV=I2R 5 What is the equation for resistance? • V/I 6 What do the symbols Q, I, t, V, P and R represent in electronics? • Q = charge in Coulombs (C) • I = current in Amperes (A) • t = time in seconds (s) • V = voltage / potential difference in Volts (V) • P = power in Watts (W) • R = resistance in Ohms (Ω) 7 For components in series, what is the total current? • In series, the current in each component is the same 8 For components in series, what is the total p.d? • The sum of the p.d.s across the components is equal to the total p.d. 9 For components in parallel, what is the total p.d? • The p.d. is the same across each component 10 For components in parallel, what is the total current? • The sum of the currents through the components is equal to the total current 11 What is the e.m.f of a source of p.d? • The electrical energy per unit charge produced by the source 12 What is a capacitor designed to do? • Designed to store charge 13 What are capacitors made up from? • Two electrical conducting plates separated by an electric insulator 14 Where do the electrons flow in a capacitor? • When the plates are connected to a battery, electrons from the negative terminal of the battery

flow onto one of the plates • An equal number of electrons leave the other plate and return to the battery via its positive

terminal

• So each plate gains an equal and opposite charge 15 What is a dielectric? • An electrical insulator 16 What is the circuit symbol for a capacitor?

17 Define capacitance • The capacitance of an object is the amount of charge it is able to store per unit potential

difference (p.d.) across it 18 What is the equation for capacitance? • 𝐶 = !

!

19 What is the unit of capacitance? • Farads • Where 1 Farad is equal to 1 coulomb of charge per volt 20 How does a capacitor store charge? • When a capacitor is connected to a direct current (d.c.) power course, charge builds up on its

plate – one plate becomes negatively charged and one becomes positively charged • The plates are separated by a dielectric, so no charge can move between them • This means that a potential difference builds up between the plates of the capacitor 20.1 What is the capacitance of a capacitor? • The charge that the capacitor can store per unit potential difference across it 20.2 What is the voltage rating of a capacitor? • The voltage rating of a capacitor is the maximum potential difference that can safely be put

across it 21 Draw a test circuit to measure the capacitance of a capacitor.

22 How would you use a test circuit to measure the capacitance of a capacitor? • Using a variable resistor, a switch, a micro-ammeter and a cell in series with the capacitor • When the switch is closed, the variable resistor is continually adjusted to keep the micro-

ammeter reading constant • At any given time, t, after the switch is closed, the charge, Q, on the capacitor can be

calculated using Q=It where I is the current • Read and record the p.d. of the capacitor at regular intervals until the capacitor has the same

voltage as the cell had originally

23 Using current and time, how would you find the charge in a capacitor? • Q=It therefore, multiplying the current and time taken for the capacitor to reach full charge, you

have the value of that charge, Q 24 How would you use charge to find the capacitance of a capacitor? • Q=CV • Therefore plot a graph of Q (in micro coulombs) against p.d. (in volts) • The gradient of this graph will be the capacitance, C, of the capacitor 25 What are typical values of capacitance for a capacitor? • Typically in the region of micro (µ) Farads • This is x10-6 26 How would you find the capacitance of a capacitor from a graph of Q against p.d? • Q=CV therefore Q/V=C • Hence, the gradient of a graph of Q against p.d. will give the capacitance 27 How would you find the capacitance of a capacitor from a graph of p.d against Q? • Q=CV therefore V/Q=1/C • Hence, the gradient of a graph of p.d. against Q will give 1/C and the reciprocal will equal the

capacitance 28 What are the problems with using capacitors instead of batteries? • Capacitors can only store small amounts of charge, therefore capacitors aren’t used instead of

batteries • To store the same energy as an AA battery, you’d need around 6000 farads • The capacitor would be massive • They also only provide power for a short time 29 What are the benefits of capacitors? • They can store charge until its needed, and then discharge all of their charge in a fraction of a

second, where as a battery would take several minutes • For this reason, charged capacitors can be dangerous 30 What are 3 uses of capacitors? 1) Camera flash – the camera battery charges the capacitor over a few seconds, and then the

entire charge of the capacitor is dumped into the flash almost instantly This allows the camera flash to be very bright for a very short time

2) Ultra capacitors can be used in back-up power supplies to provide reliable power for short periods of time

3) To smooth our variations in d.c. voltage supplies – a capacitor absorbs the peaks and fills the troughs

ENERGY STORED BY CAPACITORS 31 What is the type of energy stored as in a capacitor? • Electrical potential energy 32 How do capacitors store energy? • When a capacitor charges, one plate becomes negatively charged while the other becomes

positively charged • Like charges repel, so when each plate of the capacitor becomes charged, the charges on that

plate are being forced together ‘against their will’ • This requires energy which is supplied by the power source and stored as electric potential

energy for as long as the charges are help • When the charges are released, the electric potential energy is released 33 What graph can you use to find the energy stored by a capacitor? • You can find the energy stored by a capacitor by using the graph of potential difference against

charge for the capacitor • The p.d. across a capacitor is directly proportional to the charge stored on it, so the graph is a

straight line through the origin 34 Why does a build-up of charge on a capacitor result in a build-up of energy? • 𝐸 = ∆𝑊 = 𝑄∆𝑉 • So a build up of charge will result in a build up of energy • Because energy is proportional to charge 35 What is the work done in a capacitor equal to? • The electric potential energy stored is the work done to move the extra charge onto the plates

against the potential difference across the plates, given by 𝐸 = ∆𝑊 = 𝑄∆𝑉 • Let the small charge being moved be q • The average p.d. over that step is v • So in that small step, the energy stored is 𝐸 = 𝑞𝑣 • The total energy stored by the capacitor is the sum of all of the energies stored in each small

step increase in charge, until the capacitor is fully charged • So it’s the energy under the graph of p.d. against V 36 Hence, what is the equation for the energy stored by a capacitor? • 𝐸 = !

!𝑄𝑉

37 How can you use the equation for capacitance and the equation for the energy stored by a capacitor to create 2 further equations for energy stored?

• We know that 𝐸 = !!𝑄𝑉

• And that 𝑄 = 𝐶𝑉 • So we can derive:

1) 𝐸 = !!𝐶𝑉!

2) 𝐸 = !!!!

!

38 How does a lightning strike model a capacitor? • Imagine a thundercloud and the Earth below like a pair of charged parallel plates • Because the thundercloud is negatively charged, a strong electric field exists between the

thundercloud and the ground • The potential difference between the thundercloud and the ground, V=Ed • Where E is therefore the electric field strength and d is the height of the thundercloud above

the ground • For a thundercloud carrying a constant charge Q, the energy stored = !

!𝑄𝑉 = !

!𝑄𝐸𝑑

• If the thundercloud is forced by winds to rise to a new height d’, the energy stored is now !!𝑄𝐸𝑑′

• As the electric field is unchanged, the increase in the energy stored is !!𝑄𝐸𝑑! − !

!𝑄𝐸𝑑

• This is equal to !!𝑄𝐸∆𝑑

• The increase in the energy stored is because work is done by the force of the wind to overcome the electrical attraction between the thundercloud and the ground and to make the charged thundercloud move away from the ground

38.1 What circuit can be used to measure the energy stored in a charged capacitor and how?

• A joulemeter is used to measure the energy transfer from a charged capacitor to a light bulb when the capacitor discharges

• The capacitor p.d. V is measured and the joulemeter reading recorded before the discharge starts

• When the capacitor has discharged, the joulemeter reading is recorded again • The difference of the two joulemeter readings is the energy transferred from the capacitor

during the discharging process • This is the total energy stored in the capacitor before it discharged

• This can be compared with the calculation of the energy stored using 𝐸 = !!𝐶𝑉!

CHARGING AND DISCHARGING A CAPACITOR

39 What kind of voltage must a capacitor be connected to? • Direct current 40 Where do the electrons flow when a capacitor test circuit is turned on? • When a capacitor is connected to a d.c. power supply, a current flows in the circuit until the

capacitor is fully charged, then stops • The electrons flow from the negative terminal of the supply onto the plate connected to it 41 How is charge built up on a capacitor? • When the electrons flow from the negative terminal of the supply onto the plate connected to it,

a negative charge builds up on that plate • At the same time, electrons flow from the other plate to the positive terminal of the supple,

making that plate positive • These electrons are repelled by the negative charge on the negative plate and attracted to the

positive terminal of the supply • The same number of electrons are repelled from the positive plate as are built up on the

negative plate • This means an equal but opposite charge builds up on each plate, causing the potential

difference between the plates 42 What happens to the current in the circuit as the capacitor reaches its full

capacitance? • Initially the current through the circuit it high • As the 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 supply, the current falls to

zero (hence when the capacitor is fully charged) 43 What happens when you charge a capacitor through a resistor? • If you charge a capacitor through a fixed resistor, the resistance of the resistor will affect the

time taken to charge the capacitor • As soon as the switch is closed, a current starts to flow • The potential difference across the capacitor is zero at first, so there is no p.d. opposing the

current • The potential difference of the battery causes an initial relatively high current to flow equal to

V/R • As the capacitor charges, the p.d. across the resistor gets smaller and smaller (because the

p.d. across the capacitor is getting bigger) and so the current drops • Charge is proportional to the potential difference, so the Q-t graph is the same as the V-t graph

43.1 What test circuit would you use to investigate the charging of a capacitor?

44 What is the graph of I against t for charging a capacitor through a resistor?

45 Describe the graph of I against t for charging a capacitor through a resistor? • Initially, the current is high because the electrons can flow from the power source to the plates

and the potential difference is low, so there is no p.d. to oppose the current • However, 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 supply, the current falls to

zero • The capacitor is fully charged 46 What is the graph of V against t for charging a capacitor through a resistor?

47 Describe the graph of V against t for charging a capacitor through a resistor? • There is no potential difference of the capacitor to start with, so V is zero • As the current flows and the capacitor charges, the p.d. across the capacitor gets bigger • This is because the electrons have built up on the plates and are repelling each other, causing

a difference of charge and so a potential difference 48 What is the graph of Q against t for charging a capacitor through a resistor?

49 Describe the graph of Q against t for charging a capacitor through a resistor? • Charge is proportional to potential difference (Q=CV) • Hence, the Q-t graphs takes the same shape as the V-t graph 50 What two factors does the time taken to charge a capacitor through a resistor

depend on? 1) The capacitance of the capacitor (C). This effects 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 51 What is discharging a capacitor through a resistor? • To discharge a capacitor, take out the battery and reconnect the circuit • When a charged capacitor is connected across a resistor, the p.d. drives a current through the

circuit • This current flows in the opposite direction from the charging current • The capacitor is fully discharged when the p.d. across the plates and the current in the circuit

are both zero 52 What test circuit would you use to investigate the discharge of a capacitor?

53 What are the advantages of using a data logger in a discharge circuit? 1) Less chance of human error 2) Take more results – either take them more quickly or more slowly than humans can 3) Can record data in dangerous areas (volcanoes etc.) 4) Can record data in inconvenient areas 5) Can record data in inaccessible areas 54 Why is a voltage sensor used in a discharge circuit? • To measure the voltage across the capacitor 55 What is the graph of I against t for discharging a capacitor through a resistor?

56 Describe the graph of I against t for discharging a capacitor through a resistor? • There is a high initial p.d. across the plates of the capacitor which will cause a high current to

flow as the electrons repel each other and travel back to their start position • Over time, as the potential difference between the plates drops, the electrons flow less and the

current drops again towards zero • Although it’s the opposite

57 What is the graph of V against t for discharging a capacitor through a resistor?

58 Describe the graph of V against t for discharging a capacitor through a resistor? • There is a build up of charges repelling each other on the plates of the capacitor from when it

was charged • This creates a large p.d. • As the electrons move away from the plates and flow round the circuit, there is less and less

build up of electrons on the plate which reduces the p.d. 59 What is the equation for the voltage on a discharging capacitor?

• 𝑉 = 𝑉!𝑒!!!!"

60 What is the graph of Q against t for discharging a capacitor through a resistor?

61 Describe the graph of Q against t for discharging a capacitor through a resistor?

• Charge is proportional to potential difference (Q=CV) • Hence, the Q-t graphs takes the same shape as the V-t graph 62 What is the equation for the charge on a discharging capacitor?

• 𝑄 = 𝑄!𝑒!!!!"

63 What is the time constant of capacitance? • The time it takes for a capacitor to charge through a fixed resistor depends on R and C • The time to discharge a capacitor depends on R and C too • When the discharge time t is equal to RC, the equation becomes:

• 𝑄 = 𝑄!𝑒!!"!"

• 𝑄 = 𝑄!𝑒!! • !

!!= !

!= 0.37

• When the time t=RC, it is known as the time constant, and is the time taken for the charge on a discharging capacitor (Q) to fall to about 37% of Qo

• It is also the time taken for the charge of a charging capacitor to rise to about 63% of Qo 64 What is the equation for the time constant? • t=RC 65 What is the relationship between the resistance in series with the capacitor and the

time taken to charge/discharge the capacitor? • The larger the resistance in series with the capacitor, the longer it takes to charge or discharge • If t=RC then a larger R will result in a larger t 66 How would you find the time constant from a graph of Q, I, and V against t? • From a graph of Q against t, just find 37% of Qo and find the time taken to reach that point • From a graph of V against t, just find 37% of Vo and find the time taken to reach that point 67 What would a graph of Ln(V/V) look like? • A graph of Ln(V/Vo) against t would be a straight line with a negative gradient • The gradient is equal to − !

!"