1. Charge and current
What an electric current is
- Electric current is the rate of flow of electric charge around a circuit
- Current is measured in amperes, symbol A (often shortened to "amps")
- One ampere is the current that flows when one coulomb of charge passes a point in one second, so 1 A = 1 C/s
- For current to flow, there must be a complete (unbroken) conducting loop with a source of voltage in it, such as a cell or battery
Charge carriers in different materials
- In a metallic conductor, the moving charges are negatively charged electrons; the heavy positive metal ions are fixed in a lattice and only the outermost electrons drift through it
- In a liquid electrolyte or ionised gas, the moving charges include both positive and negative ions, which drift in opposite directions
Conventional current vs electron flow
- Long before electrons were discovered, scientists agreed that current flows from the positive terminal of a cell, around the external circuit, and back to the negative terminal. This historical choice is called the direction, and it is the direction shown by every arrow on every circuit diagram in exam questions
- In a metal wire, the electrons actually drift the other way, from the negative terminal, through the wire, back to the positive terminal
- Both descriptions refer to exactly the same physical situation; they just measure the flow in opposite senses. In exam answers, always use the conventional direction unless asked for electron flow explicitly
Measuring current
- An ammeter is the instrument that measures current
- An ammeter must be wired in series with the component whose current is being measured, because the same current that flows through the component must also flow through the ammeter
- An ideal ammeter has zero , so inserting it does not affect the circuit it is measuring
The charge equation
Q = I × t
- where:
- Q = charge that has passed (coulombs, C)
- I = current (amps, A)
- t = time the current has been flowing (s)
- Rearrangements:
- I = Q / t (current is charge per second)
- t = Q / I
- Convert any milliamp values into amps before substituting: 1 mA = 1 × 10⁻³ A. A current of 250 mA, for example, is 0.250 A
Common exam question
Calculating charge, current or time with Q = It
Question: Calculate the charge transferred, the current, or the time taken, using charge = current × time, sometimes with the answer wanted in a stated unit (2–3 marks).
Set in 6 of the 24 papers. The marks are for the substitution or rearrangement (one scheme gives each its own mark when you solve for the current), the evaluation, and then whatever the question adds: a unit (coulombs or C, marked on its own) or a conversion. Times are often given in hours or milliseconds, or the answer is wanted in minutes; each conversion is a separate mark, awarded independently of the arithmetic, so 1 hour becomes 3600 s before you multiply and seconds are turned into minutes only at the end. A power-of-ten slip costs one mark, and an answer written with a prefix such as nC is accepted.
Worked example
Calculating charge from current and time
A torch bulb carries a current of 0.40 A for 30 s. Calculate the charge that passes through the bulb.
Solution:
- Write the equation: Q = I × t
- Substitute: Q = 0.40 × 30
- Q = 12 C
2. Voltage and energy
What voltage is
- Voltage (also called ) between two points in a circuit is the energy transferred per unit charge that passes between those two points
- Voltage is measured in volts, symbol V
- One volt is the voltage between two points when one joule of energy is transferred for every coulomb of charge that moves between them, so 1 V = 1 J/C
- "Potential difference" emphasises that voltage is always a difference between two ends; like temperature difference or height difference, it only makes sense as a comparison between two points
Common exam question
Defining voltage and current
Question: State the meaning of voltage, or of electric current (1 mark).
Asked in 2 of the 24 papers, once for each. For voltage the mark is for energy transferred per unit charge: "work done" may replace energy transferred and "per coulomb" may replace per unit charge, but V = E/Q on its own earns it only if you define every term. For current, write the rate of flow of charge, or the charge passing per second: "rate of flow of electrons" is ignored and scores nothing.
A third paper tests the volt in multiple-choice form: it is a joule per coulomb, not a joule per second (the watt) or a coulomb per second (the ampere).
Where charges gain and lose energy
- A charge gains energy when it is pushed through the cell by the chemical reaction inside; this is the cell doing work on the charge
- A charge loses energy when it passes through a component such as a bulb, a heater or a motor; this is the charge doing work on the surroundings, transferring its energy to light, internal energy of the surroundings, or kinetic energy
- Around a full loop, the total energy gained at the cell exactly equals the total energy lost in the rest of the circuit. This is conservation of energy applied to electricity
- Numerical intuition: a 9 V battery gives each coulomb that crosses it a 9 J energy boost; if that same coulomb then traverses a single 9 V bulb on the way back round, it hands the full 9 J to the bulb's filament
Measuring voltage
- A voltmeter is the instrument that measures voltage
- A voltmeter must be wired in parallel with the component whose voltage is being measured, so its two leads sit on either side of the component, reading the voltage across it
- An ideal voltmeter has infinite , so no current is diverted through it and the rest of the circuit is undisturbed
- Practical tip: build the rest of the circuit first, get it working, then clip the voltmeter across the chosen component. This avoids confusing yourself with the voltmeter mid-build
Common exam question
Adding an ammeter or voltmeter to a circuit diagram
Question: Draw a circuit diagram for an investigation, or add a meter to a given circuit, so that the current in a component and the voltage across it can be measured (1–4 marks).
Asked in 11 of the 24 papers, as anything from a one-mark addition to a four-mark circuit diagram. The ammeter goes in series with the component (for the current in the cell, on the main branch of the circuit) and the voltmeter in parallel with that component alone. Each placement is a mark, and the symbols are marked too: a voltmeter drawn across both the component and the variable resistor is rejected, and one scheme withholds the complete-circuit mark for extra components.
The energy-charge-voltage equation
E = Q × V
- where:
- E = energy transferred (J)
- Q = charge that has moved (C)
- V = voltage between the two points (V)
- Rearrangements:
- V = E / Q (voltage is energy per coulomb, straight from the definition)
- Q = E / V
Common exam question
Calculating energy, charge or voltage with E = QV
Question: Calculate the energy transferred, the charge or the voltage using energy transferred = charge × voltage (3 marks).
Set in 4 of the 24 papers. Finding charge or voltage earns a mark each for substitution, rearrangement and evaluation; a power-of-ten slip costs one. The data usually come in standard form or with a prefix, so turn millijoules into joules before you evaluate: one scheme ignores unit conversions until the evaluation mark, so a missed conversion costs that mark. Writing the formula in symbols is fine, but C stands for coulombs: a "C" written for charge is rejected in two of these schemes and ignored in a third, so use Q.
When a question asks how long a lamp takes to transfer a given energy at a given voltage, the expected route is energy = current × voltage × time, but the scheme also accepts finding the charge from E = QV and then the time from Q = It.
3. Resistance
What resistance is
- Resistance is the opposition a component offers to the flow of electric current through it
- The greater the resistance, the harder it is for charge to flow, and so the smaller the current for a given voltage
- Resistance is measured in ohms, symbol Ω (the Greek capital omega)
- A component has a resistance of 1 Ω when a voltage of 1 V across it drives a current of exactly 1 A through it (so 1 Ω = 1 V/A)
What sets the resistance of a component
- Material: good conductors like copper and silver have very low resistance; insulators like rubber and dry wood have enormous resistance
- Length: a long wire has more resistance than a short one of the same material and thickness, because every extra metre adds to the obstruction
- Cross-sectional area: a thick wire has less resistance than a thin one, because there is more room for charge to flow
- Temperature: in most metals, resistance rises as temperature rises; the metal ions vibrate harder and collide with the drifting electrons more often
- Even the connecting wires themselves have a small resistance, but in exam circuits they are taken to be zero unless the question states otherwise
Ohm's law: V = I × R
- The defining equation linking voltage, current and resistance is:
V = I × R
- where:
- V = voltage across the component (V)
- I = current through the component (A)
- R = resistance of the component (Ω)
- Rearrangements:
- I = V / R (current is voltage divided by resistance)
- R = V / I (resistance is voltage divided by current, which is the experimental way to measure R)
- A component is said to be ohmic if its resistance is constant across the working range (V is then directly proportional to I). Many resistors and lengths of metal wire at a steady temperature behave this way; filament lamps and diodes do not, and so are non-ohmic (covered fully in topic 06)
Common exam question
Stating the formula linking three quantities
Question: State the formula that links voltage, current and resistance, or charge, current and time, or energy transferred, charge and voltage (1 mark).
Asked in 12 of the 24 papers, most often for voltage = current × resistance. Words or standard symbols both score, in any rearrangement: V = I × R, Q = I × t or E = Q × V, or I = V/R and the like. Two habits can lose the mark. A formula written in units, such as V = A × Ω, is not a formula and is ignored. And C is the symbol for coulombs, not for current: schemes at best ignore a "C" written for current or charge and at worst reject it, so use I for current and Q for charge.
Common exam question
Calculating current, voltage or resistance with V = IR
Question: Calculate the current in a component, the voltage across it or its resistance, sometimes from a current read off a graph or with the unit to give (2–5 marks).
Set in 9 of the 24 papers. For the current or the resistance, the three-mark version gives one mark each for substitution, rearrangement and evaluation; R = V/I written anywhere in the working earns the rearrangement mark, and a power-of-ten slip costs one mark, so an answer out by a factor of a thousand still scores two. Convert mA to A and kΩ to Ω before substituting; one scheme makes that conversion its own mark.
When the current must be read from a graph at the stated voltage, the reading has a small tolerance and, in the five-mark version, a mark of its own. When the component shares the supply with another, use the voltage across the component itself: the supply voltage minus the voltage across the other component.
Worked example
Finding resistance from voltage and current
A resistor has a voltage of 9.0 V across it and a current of 0.30 A through it. Calculate its resistance.
Solution:
- Write the equation: V = I × R, so R = V / I
- Substitute: R = 9.0 / 0.30
- R = 30 Ω
Idealisations on circuit diagrams
- In exam questions, unless stated otherwise:
- the wires have zero resistance
- the internal of the cell or battery is zero
- an has zero resistance and so does not alter the current it is reading
- a has infinite resistance and so draws no current away from the component it is reading
- These idealisations make the algebra clean; in real life, every one of them is a small approximation rather than an exact truth