1
Q
How do we define electrical current?
A
The rate of flow of electrical charge. Represented by the symbol I, and measured in amperes.
2
Q
What equation links current, charge and time?
A
I = dQ/dt. We can think of this as ‘current is the number of coulombs of charge passing a point over a given time’.
3
Q
What are the base and derived units of electrical charge?
A
Coulombs (Q) and, from the equation I = dQ/dt, ampere-seconds (A s).
4
Q
What types of particles can be considered charge carriers?
A
Electrons (in wires) and charged ions (in electrolytic solutions)
5
Q
What is the value of the elementary charge e, and what does it represent?
A
This is given as 1.6 * 10^-19 C, and this represents the charge on one proton, from which all relative charges such as that of an electron, or a charged ion, are derived from.
6
Q
Why do we describe the charge on an object as quantised?
A
Charges must always be multiples of 1.6 * 10^-19 (the elementary charge) so there is a limited set of values charge can have. Therefore, the value of charge is ‘quantised’.
7
Q
How can we express the net charge on an object?
A
This must always be some multiple of e, and we calculate it using the equation Q=+-ne, where n is the number of electrons and Q is the charge passing through the given point per second.
8
Q
How do most objects obtain a net charge?
A
- Most of the time, a net charge on an object arises due to the gain or loss of electrons by the object.
- If the object starts in a neutral state, if it gains electrons, it will gain an overall negative charge.
- The opposite happens if electrons are lost.
9
Q
What are the charge carriers when current flows in the solid state?
A
Electrons are the charge carriers in the solid state.
10
Q
What are the charge carriers when current flows in the liquid state?
A
Charged ions are the charge carriers in the liquid state.
11
Q
How might we model the flow of charge through a (metallic) wire?
A
- The wire itself has a metallic lattice structure, with a pool of delocalised electrons surrounding positive metal ions.
- If the wire becomes charged on opposite ends, the electrons will be drawn towards the oppositely-charged positive end, hence the charge carriers move and current flows.
12
Q
What factors might cause an increase in current?
A
We can think about this using the equation I=dQ/dt…
- A greater number of electrons per second flowing increases the current (this might be caused by increased cross-section)
- The same number of electrons moving past a point more quickly increases the current
13
Q
What is the difference between conventional current and electron flow?
A
- Conventional current flows between positive - negative termini.
- Electron flow runs in the reverse direction
14
Q
What do we call a liquid that can carry an electrical current?
A
These are called electrolytes, and are used in the process of electrolysis, wherein an ionic solution is split into positive and negatively charged ions which are attracted to oppositely-charged electrodes.
15
Q
How does electrolysis result in the flow of an electric current?
A
- The ionic solution (salt) splits into +ve metal ions and -ve non-metal ions
- These are attracted towards -ve and +ve electrodes respectively
- This is the movement of charge carriers, so a current flows through the electrolyte
- The +ve metal ion accepts an electron, which is donated by the -ve non-metal ion when it reaches an electrode. This flow of electrons causes a current to flow in the metal circuit.
16
Q
Ideally, should ammeters have a high or low resistance?
A
They should have a low resistance. They are connected in series to the rest of the circuit, so a lower resistance would reduce the effect they have on the size of the current.
17
Q
What discovery did Millikan’s experiment help him to make?
A
It proved that electrical charge is a quantised value, through investigation the motion of droplets between oppositely-charged metal plates.
18
Q
How did Millikan’s experiment work?
A
- When the oil droplets were sprayed they experienced air resistance, upthrust and gravitational force.
- Some were held stationary as the force of gravity = the electrostatic force of the charged plates
- Some drifted slowly through the induced electric field of the plates.
19
Q
Describe the law of conservation of charge.
A
Electrical charge can neither be created nor destroyed, so the total amount of charge in the universe is constant
20
Q
What is Kirchhoff’s 1st Law?
A
For any point/junction in an electrical circuit, the sum of currents into that point is equal to the sum of currents flowing out of the point
21
Q
How do we classify conductivity of a material?
A
Conductivity is based on a material’s number density. The higher the number density, the greater number of free electrons per unit volume, so the electrical conductivity increases.
22
Q
What is the definition of number density?
A
This is the number of free charge carriers per unit volume in a material.
23
Q
What is the (functional) difference between a conductor and a semiconductor?
A
- Semiconductors have a much lower number density than conductors.
- This means that, in order to carry the same current, more charge must flow per unit time, so the electrons must be moving more quickly for a constant cross-section.
- This incidentally causes the temperature of a semiconductor to increase.
24
Q
Do charge carriers move at a high or low velocity?
A
Although the effects of charge flowing seem instant, charge carriers actually move at a relatively slow velocity. This is because free electrons collide frequently with metal ions, so their path is very indirect and therefore their velocity is very low overall.
25
What equation links current, cross sectional area, number density, elementary charge and mean drift velocity?
I=Anev, often rearranged as I=nAve for memorability.
26
What is the definition of *mean drift velocity*?
The average velocity of electrons as they travel through a given medium, colliding with +ve metal ions.
27
How does cross-sectional area affect mean drift velocity?
We can consider the equation I=nAve. The narrower the wire (i.e. the smaller the cross-sectional area), the greater the drift velocity must be in order to maintain a constant value of current.
28
How do we define *potential difference*?
Potential difference is a measure of energy transferred to other stores by charge carriers in a circuit, per coulomb of charge. It is measured in Volts.
29
What equation links voltage, energy transferred and charge?
V = E/Q
30
What are the base and derived units for voltage?
- Volts (V)
- Joules per coulomb (J C^-1)
31
Why are voltmeters connected in *parallel* to the rest of the circuit?
- Voltmeters have high resistance so that, in parallel, their resistance has little effect on the current passing through the main loop of the circuit.
- If connected in series, this high resistance would significantly reduced the current.
32
What is the difference between *potential difference* and *electromotive force*?
- Potential difference describes when work is done by the charges i.e. energy is transferred *to* other stores.
- EMF is used to describe when work is done on charge carriers, i.e. energy is transferred *from* other stores *to* the charges.
33
Give some examples of sources of EMF (electromotive force).
- Solar cells
- A dynamo
- Thermocouples
34
What is an electron gun?
This is an electric device which produces a narrow beam of electrons, used to ionise particles through the addition/removal of electrons.
35
Summarise how an electron gun works.
- A metal wire is heated by a current such that thermionic emission occurs, and electrons are released into a vacuum containing an anode with a hole.
- The electrons accelerate towards the anode, gaining kinetic energy.
- The hole ensures that electrons exit the electron gun with specific kinetic energy.
36
How can we link work done on an electron to its gain in kinetic energy?
- The work done on a single electron as it accelerates = elementary charge * accelerating p.d. (eV)
- This is equal to kinetic energy due to the law of conservation of energy.
- Therefore eV=1/2*mv^2
37
How does the kinetic energy of electrons change with accelerating p.d.?
The greater the p.d., the more energy is transferred to electrons, so they move faster (i.e. with more kinetic energy).
38
How do we define *resistance* of a component?
The resistance of a component is the ratio between the the p.d. across the component and the current flowing through it.
39
What is the equation linking resistance, current and voltage?
R = V/I
- Where R is given in Ohms, V is given in Volts and I is given in Amperes
40
What is the definition of an Ohm?
The resistance of a component when a potential difference of 1V occurs per ampere of current passing through
41
Describe Ohm's law.
For a metallic conductor maintained at a constant temperature, the current in the wire is directly proportional to the potential difference across its ends.
42
How does the current through a wire affect its resistance, and why?
When we increase current through a wire whilst maintaining a fixed potential difference, the temperature of the wire increases.
- This occurs because charge carriers collide more frequently with positive ions in the wire, causing them to do more work, inhibiting the flow of current.
- This causes resistance to increase.
43
What is the shape of the I-V graph of a fixed resistor, and what does this tell us about...
- Ohmic properties?
- Changes in resistance with current?
- The shape is a straight line passing thru. the origin
- This is an Ohmic conductor
- Resistance is constant - I is proportional to V
44
What is the shape of the I-V graph of a filament lamp, and what does this tell us about...
- Ohmic properties?
- Changes in resistance with p.d.?
- The shape is a curve passing thru. the origin
- This is a non-Ohmic component
- Resistance increases with p.d., due to an increase in temperature of the wire
45
Why are light-emitting diodes more useful today than filament lamps?
They transfer electrical energy directly into light through a different process to filament lamps - i.e., they do not increase in temperature in order to achieve light emission. This means that they are able to achieve the same result considerably more efficiently, drawing much less power.
46
What is the shape of the I-V graph of a semiconducting diode, and what does this tell us about...
- Ohmic properties?
- Changes in resistance with p.d.?
- The shape is a flat line until the threshold p.d., after which the line curves
- This is a non-Ohmic component
- Resistance is very high in the reverse bias and remains so until the threshold p.d. at around 0.7V usually, before significantly decreasing
47
How do diodes only enable a current to flow in one direction (polarity)?
The resistance of a diode is (infinitely) high when a potential difference is applied in the reverse direction. This means that the diode is unable to conduct electrical current.
48
What factors can affect the resistance of a component?
- The material it is made from
- The length of the wire
- The wire's cross-sectional area
49
What is the difference between resistance and resistivity?
Resist*ance* considers a specific component, whereas resist*ivity* is used to describe an electrical property of a material.
50
How is resistance linked to...
- Length?
- Cross-sectional area?
- Resistance and length of wire are proportional.
- Resistance is inversely proportional to the cross-sectional area of a wire.
51
What is the equation for resistivity? From this equation, determine the units of resistivity.
resistivity = (resistance * cross-sectional are) / length of wire, where resistivity is given in units ohm-metres
52
How can we define *resistivity*? Consider its equation.
The resistivity of a material at a constant temperature is the product of the resistance of a component made from the material and its cross-sectional area, divided by length
This makes resistivity a *constant of proportionality* for a material
53
What is the difference in resistivity between conducting and insulating materials?
Conductors have resistivity of the order of 10^8 ohm-metres, compared to 10^16 ohm-metres for insulators. Semiconductors fall between these values.
54
What characterises a thermistor?
It is a component made from a semiconducting material with a negative temperature co-efficient. As the temperature of the thermistor increases, its resistance drops significantly.
55
What is meant by a negative temperature coefficient?
The resistance of the component drops as its temperature increases.
56
Explain why resistance decreases with an increase in temperature for a thermistor.
- In semiconducting materials, as the temperature of the material increases, the number density of the charge carriers also increases.
- Therefore, resistance must decrease as current increases.
- This is called a negative temperature co-efficient.
57
What is the definition of electrical power?
The rate of energy transfer by an electrical component, measured in Watts.
58
What equation links power, current and voltage? How could this be further derived using V=IR?
P=IV, where power is measured in Watts, I is current in Amperes and V is voltage in Volts.
- We could derive this as P=I^2R or P=V^2/R
59
What equation links power, energy transferred and time?
P=W/dt, which can we used to allow us to calculate W=VIt
60
What factors does the energy transferred to a component depend on?
The power rating of the component, and the time it is used for.
61
What is the definition of a kilowatt-hour?
The energy transferred by a device with power 1kW operated over 1 hour
62
Summarise Kirchhoff’s Second Law.
In any single closed loop of a circuit, the sum of electromotive forces is equal to the sum of potential differences.
63
What can we say about current and potential difference in a *series* circuit?
Any series circuit has just one closed loop.
- By Kirchhoff’s 1st Law: current must stay constant throughout.
- By Kirchhoff’s 2nd Law: the total emf if shared proportionally between all of the components.
64
What can we say about current and potential difference in a *parallel* circuit?
A parallel circuit provide more than one possible path for charges.
- By Kirchhoff’s 1st Law: the sum of currents entering a junction = current leaving. This is defined by resistance
- By Kirchhoff’s 2nd Law: since sum of emfs = sum of pd in a closed loop, so. the total pd across each branch equals the input emf
65
If two identical components are connected in series in a circuit, what can we say about how the emf is shared between them?
The two components will be of identical resistance. This means that the total sum of the electromotive force in the circuit will be shared equally between the two components.
66
If a (parallel) circuit has more than one branch/loop, what can we say about the potential difference in the circuit?
- The potential difference in each ‘loop’ is equal to the electromotive force, and is independent of that of the other loop.
- This means that whatever components we add to one branch does not affect the voltages within the other branch.
67
Describe the trend with resistors added in *series*. Include an equation.
R(total)=R1+R2+R3…+Rn
Essentially the total resistance R in a closed loop of a series circuit is equal to the sum of the resistances of components connected to it, since each added resistor effectively ‘increases the length’ of the singular path of the charges.
68
Describe the trend with resistors added in *parallel*. Include an equation.
1/R= 1/R1+1/R2…+1/Rn
Essentially each resistor we add provider another 'path' for current to take. This effectively reduces the cross-sectional area, reducing overall resistance as more resistors are added in succession.
69
Why do car batteries have a very low internal resistance?
So they can readily supply the high currents required to operate the starter motor of a car.
70
Why do *lost volts* occur at the power source, giving rise to a lower terminal p.d.?
- The charges do work as they move through the power sources
- This means that not all of the electromotive force (energy transferred) is available to the rest of the circuit
- This means that terminal p.d. is less than the original emf.
71
What equation links emf, terminal p.d. and lost volts?
Electromotive force = terminal p.d. + lost volts
72
How does terminal p.d. differ from electromotive force?
Electromotive force does not consider the lost volts arising due to the internal resistance of the power supply. Terminal p.d. instead is measured from the termini of the power source, and describes how much of the total emf is available for the rest of the circuit to use.
73
What happens to terminal p.d. and lost volts when the current increases.
- As current increases, more work is done per unit time by the charges passing through the power source.
- This means that the value of lost volts must increase by V=Ir.
- Since terminal p.d. = emf - lost volts, the terminal p.d. must decrease as a result.
74
How do we calculate lost volts given the internal resistance of a power supply?
Lost volts (V) = current (I) * internal resistance (r)
- Here, note that internal resistance is denoted by a lower case ‘r’.
75
What equations can we use to calculate the emf from a power source?
EMF = terminal p.d. + lost volts
Therefore - EMF = V+Ir, so EMF=IR+Ir
Taking out a factor of I - EMF=I(R+r)
76
If a circuit diagram does not include terminal p.d., what should we assume in regards to this?
The power supply must be of negligible internal resistance, so we do not need to factor this into our calculations
77
How could we practically investigate internal resistance? Describe a method.
- Connect a voltmeter across a power supply (cell) and an ammeter to the rest of the circuit in series with a variable resistor.
- We could record values of terminal p.d. by drawing varying values of current from the power supply.
- These results could then be plotted on a graph. Re-arranging emf=V+Ir we get V=-rI+emf. Gradient = r and y-intercept = emf
78
Why must we ensure that current does not become too high when investigating internal resistance?
If current becomes too high, the temperature of the cell will increase, increasing the internal resistance above the constant that we expect. This is because the increased rate of flow of charge causes more work to be done per second by the charges flowing through the cell, increasing thermal losses
79
How can a high internal resistance act as a safety measure?
A high internal resistance limits the current being supplied in high-voltage environments. This reduces the possibility of a fatal current being passed through someone if a fault develops.
80
Why do mobile phone batteries often have a low internal resistance?
- The battery can take in higher currents without the associated dissipation of energy to thermal stores
- So more energy overall is transferred to the chemical stores in the battery.
- This reduces recharging time
81
Should cells be connected in series or in parallel to maximise *current*?
- If we connected cells in *series*, the total emf would increase, but the increase in current would be inhibited by the internal resistance of the cells
- However, the internal resistance is considerably smaller in *parallel*, whilst the supplied emf remains the same, so a higher current is delivered
82
What does a potential divider circuit do?
These use fixed or variable resistors to alter the potential difference across an output from that of the input electromotive force.
83
How does a potential divider circuit work?
- We know that the p.d. across each resistor in series depends on the ratio of total resistances
- We can use this to provide our desired p.d. across a resistor, to which we can connect an output circuit in parallel which then supplies the same p.d
84
How can we express the ratio of resistances and their related potential differences algebraically?
V1/V2=R1/R2
85
What is the potential divider equation?
V(out)=V(in)*R2/(R1+R2…)
86
Explain the effect of *loading* a potential divider.
- We connect a component or circuit to our V(out) in parallel with the related resistor.
- R(combination) decreases. This alters the ratio of resistances, such that the loaded combination receives a lower proportion of the total emf, so v(load) falls
- The parallel resistors equation shows that adding a high load resistance has little effect on V(load)
87
If we want to *maximise* V(load) when loading a potential divider, should the load be of high or low resistance?
The load circuit should be high resistance. This is because adding a resistor of high resistance in parallel has little effect on R(combination) so the ratio of potential differences is largely unaffected.
88
How do sensing circuits produce a varying V(out)?
- One of the resistors in series, from which V(out) is tapped off, should be replaced with a component whose resistance can change. This could be a variable resistor, LDR, thermistor, etc.
- This will therefore allow us to vary the ratio of resistances.
- This will in turn enable V(out) to vary as resistance changes.
89
How might we produce a light sensor using sensing circuits?
- We could produce a series circuit containing an LDR and a fixed resistor.
- A load component could be connected to V(out) in parallel with the fixed resistor.
- As light intensity increases, resistance of the LDR decreases, and the fixed resistor receives a greater share of the EMF, so V(out) increases, supplying larger current.
90
How do potentiometers work?
A potentiometer has 3 terminals - input A, output B and a sliding contact.
- When the contact slides towards A, V(out) increases since the resistance between the contact and B (across which V(out) is connected in parallel) is higher.
- When the contact moves towards B, V(out) decreases until it reaches zero when it reaches B, for the same reason.
91
Why might a potentiometer be more useful than a potential divider in some circumstances?
Potentiometers can be made considerably more compact. They can be constructed to provide linear or logarithmic changes in V(out). They also provide a wider range of V(out) from zero to max.
