Electricity and D.C. circuits

9. Electricity

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9. Electricity — Cambridge AS & A Level Physics 9702 — CAMBRIDGE AS & A LEVEL PHYSICS 9702 — COMPLETE NOTES notes: Use current, charge, potential difference, power, resistance, Ohm's law, I–V characteristics, resistivity and sensor resistors to analyse electrical circuits.Electri…

Electric current
Conventional current
Quantisation of charge
Charge carriers
Drift speed
Carrier sign

Section 1 of 11Electric current

Electric current

Electric current the flow of charge carriers, measured in amperes (A).

Charge carriers can be positive or negative.

Conventional current

Conventional current the flow of positive charge from the positive terminal to the negative terminal.

It is opposite to the electron flow in a metal, because it was defined before electrons were discovered.

Ammeter

Ammeter it measures current and is always connected in series.

Quantisation of charge

Quantisation of charge charge occurs in multiples of the elementary charge e = 1.60 × 10⁻¹⁹ C.
- (electron −e, proton +e)

Section 2 of 11Charge and current

Equation

Equation current is the charge passing per unit time, I = Q/t, so Q = It, with charge in coulombs.

Sign

Sign conventional current is the flow of positive charge, so current is given as a positive value.

Section 3 of 11Current in a conductor

Charge carriers

Charge carriers in a metal they are free electrons, and drift speed is their average speed along the wire.

Drift speed

Drift speed it is very slow, about a millimetre to a centimetre per second, yet current appears instantaneously because the number density of carriers is huge.

Equation

I = Anvq.
A is the cross-sectional area (m²) and n the number density of carriers (m⁻³).
v is the average drift speed (m s⁻¹) and q the charge of each carrier (C).

Carrier sign

Carrier sign the same equation is used for positive or negative carriers, which have the same effect, so the positive-charge model works.

Section 4 of 11Potential difference and power

Potential difference and power

Potential difference (p.d.)

Potential difference (p.d.) the energy transferred per unit charge as it moves from one point to another, V = W/Q.

A cell makes one end of a circuit positive and the other negative, setting up a p.d.

Unit

Unit the volt, 1 V = 1 J C⁻¹, so a 3 V bulb receives 3 J from each coulomb.

Voltmeter

Voltmeter it measures p.d. and is always connected in parallel across the component.

Series circuit

Series circuit the supply p.d. is shared between the components.

Parallel circuit

Parallel circuit each branch has the supply p.d.

Brightness

Brightness with the same current, a 240 V lamp transfers 20 times as much energy per coulomb as a 12 V lamp.

Power

Power the rate of doing work, P = IV.

What the symbols mean: P = power (W) · I = current (A) · V = potential difference (V)

Substituting V = IR gives P = I²R, and substituting I = V/R gives P = V²/R.
For a fixed resistance, doubling the current or p.d. makes the power four times greater.

Section 5 of 11Resistance and Ohm's law

Resistance

Resistance the opposition to current, R = V/I, measured in ohms (1 Ω = 1 V A⁻¹).

For a given p.d., a higher resistance gives a smaller current.
All components, including wires, have some resistance.

Ohm's law

Ohm's law for a conductor at constant temperature, the current is proportional to the p.d. across it.

Test for ohmic behaviour

Test for ohmic behaviour the I–V graph is a straight line through the origin, and the resistance is 1/gradient.

Measuring resistance

Measuring resistance use a low supply voltage (1 to 2 V) to avoid heating.
Connect the component with an ammeter in series and a voltmeter in parallel.
Use a variable resistor to change the current and record pairs of V and I.
Plot I against V and take R = 1/gradient.

Section 6 of 11I–V characteristics

Component	Graph	Reason
Metal conductor at constant temperature (resistor)	Straight line through the origin	Resistance is constant
Filament lamp	S-shaped curve that flattens at high V	The filament heats, so resistance increases and current rises more slowly
Semiconductor diode	Almost zero current in reverse bias; sharp rise above about 0.7 V in forward bias	It conducts in one direction only

I–V characteristics

Straight line

Straight line constant resistance; a curve means resistance is changing.

Resistance at a point

Resistance at a point it is V/I at that point, not the gradient of a curve.

Forward bias

Forward bias current in the direction of the arrowhead symbol.

Reverse bias

Reverse bias the diode does not conduct, so current is zero.

Section 7 of 11Resistance and temperature

Heating mechanism

Heating mechanism free electrons collide with vibrating metal ions and transfer kinetic energy to them, so the wire heats.

Temperature effect

Temperature effect a higher temperature gives larger vibrations and more collisions, so more resistance and less current.

Filament lamp

Filament lamp this is why its resistance rises as it gets hotter.

Section 8 of 11Resistivity

Resistance of a wire

R = ρL/A, where ρ is the resistivity (Ω m), L the length and A the cross-sectional area.
A longer wire has more resistance and a thicker wire has less.
For a circular wire A = πd²/4, so doubling the diameter quarters the resistance.

Resistivity

Resistivity a property of the material that depends only on temperature, and a higher value means more resistance.

Material	Resistivity / Ω m
Copper	1.7 × 10⁻⁸
Gold	2.4 × 10⁻⁸
Aluminium	2.6 × 10⁻⁸
Germanium	0.6
Silicon	2.3 × 10³
Glass	10¹²
Sulfur	10¹⁵

Copper

Copper it is used in wires because of its low resistivity.

Insulators

Insulators their resistivity is so high that virtually no current flows.

Section 9 of 11Sensor resistors

1Light-dependent resistor (LDR)

Light-dependent resistor (LDR) a non-ohmic sensor whose resistance falls as light intensity rises.
In the dark it has millions of ohms and in bright light only tens of ohms.
It switches on street lights and garden lights at dusk.
At constant light intensity its I–V graph is a straight line.

2Thermistor (NTC)

Thermistor (NTC) a non-ohmic sensor whose resistance falls as temperature rises and rises as it cools.
It is used in ovens, fire alarms and digital thermometers.
In series with a fixed resistor, cooling raises its resistance, lowers the current and increases its share of the p.d.

Section 10 of 11Key terms

Term	Meaning
Electric current	The rate of flow of charge, I = Q/t.
Conventional current	The direction of flow of positive charge, from positive to negative.
Potential difference	Energy transferred per unit charge between two points, V = W/Q.
Resistance	The opposition to current, R = V/I.
Ohm's law	At constant temperature, current is proportional to p.d.
Resistivity	A property of a material in R = ρL/A, measured in Ω m.
Drift speed	The average speed of charge carriers along a conductor.
Thermistor	A temperature-sensitive resistor whose resistance falls as temperature rises (NTC).
LDR	A light-dependent resistor whose resistance falls as light intensity rises.

Section 11 of 11Exam technique

Drawing conventional current in the direction of electron flow — it goes from positive to negative.

Connecting a voltmeter in series or an ammeter in parallel — voltmeters are parallel, ammeters series.

Calling a filament lamp ohmic — its resistance rises with temperature, so its I–V graph curves.

Taking resistance as the gradient of a curved I–V graph — use V/I at the point, and 1/gradient only for a straight line.

Forgetting to convert mm² to m² or using the diameter in πr² — use the radius.