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3.2.3 Current, potential difference and resistance

Current

Definition

Electric current

The rate of flow of electric charge.

  1. Current, symbol III, is the rate of flow of charge around a circuit.
  2. Current is measured in amperes, unit A\text{A}A, often shortened to amps, using an ammeter connected in series.
  3. Small currents are often given in milliamperes, where 1 mA=0.001 A1\ \text{mA} = 0.001\ \text{A}1 mA=0.001 A.
  4. A current can only flow when there is a closed circuit and a source of potential difference, such as a cell, to push the charge around it.

Potential difference

Definition

Potential difference

The energy transferred per unit charge as the charge passes between two points in a circuit.

Definition

Volt

The unit of potential difference, equal to one joule of energy transferred for each coulomb of charge.

  1. Potential difference, symbol VVV, is the energy transferred per unit charge as the charge moves between two points in a circuit.
  2. Potential difference is measured in volts, unit V\text{V}V, using a voltmeter connected in parallel across the component.
  3. The definition can be written as an equation, V=EQV = \dfrac{E}{Q}V=QE​, where EEE is the energy transferred in joules, J\text{J}J, and QQQ is the charge in coulombs, C\text{C}C.
    1. This means that 1 V=1 J/C1\ \text{V} = 1\ \text{J/C}1 V=1 J/C, so a potential difference of 1 V1\ \text{V}1 V transfers 1 J1\ \text{J}1 J of energy for every coulomb of charge.
  4. The potential difference across a cell tells you how much energy the cell gives to each coulomb of charge that passes through it.
    1. A 9 V9\ \text{V}9 V battery gives each coulomb of charge 9 J9\ \text{J}9 J of energy.
  5. The potential difference across a component tells you how much energy each coulomb transfers in that component, for example to the thermal store of a resistor or away from a lamp by light.
  6. The potential difference of the supply is what drives charge around a circuit, so a larger supply potential difference pushes more charge through a component every second.

Resistance

Definition

Resistance

A measure of how much a component opposes the flow of charge through it.

Definition

Ohm

The unit of resistance, equal to the resistance of a component that carries a current of one ampere when the potential difference across it is one volt.

  1. Resistance, symbol RRR, is a measure of how strongly a component opposes the flow of charge through it.
  2. Resistance is measured in ohms, unit Ω\OmegaΩ, and large resistances are often given in kilohms, where 1 kΩ=1000 Ω1\ \text{k}\Omega = 1000\ \Omega1 kΩ=1000 Ω.
  3. In a metal, the current is a flow of free electrons, which keep colliding with the ions that make up the metal.
    1. Each collision slows the electrons down and transfers energy to the ions, so the more often the electrons collide, the greater the resistance.
  4. Connecting wires are made of copper and have a very small resistance, while resistors are made to have a particular, much larger resistance.

How the three quantities are linked

  1. The current through a component depends on both the potential difference across it and its resistance.
  2. For a component with a fixed resistance, a larger potential difference produces a larger current, because each coulomb is pushed through with more energy.
  3. For a fixed potential difference, a larger resistance produces a smaller current, because the component opposes the flow of charge more strongly.
  4. The resistance of a component is found by dividing the potential difference across it by the current through it, R=VIR = \dfrac{V}{I}R=IV​.
    1. To find a resistance, the potential difference and the current must be measured at the same time on the same component.
  5. Current: symbol III, measured in amperes, A\text{A}A, with an ammeter in series.
  6. Potential difference: symbol VVV, measured in volts, V\text{V}V, with a voltmeter in parallel.
  7. Resistance: symbol RRR, measured in ohms, Ω\OmegaΩ, and calculated from readings of VVV and III.
Example

Finding a resistance from meter readings

  • A voltmeter across a resistor reads 6.0 V6.0\ \text{V}6.0 V, and the ammeter in series with it reads 0.30 A0.30\ \text{A}0.30 A.
R=VI R = \dfrac{V}{I} R=IV​ R=6.0 V0.30 A=20 Ω R = \dfrac{6.0\ \text{V}}{0.30\ \text{A}} = 20\ \Omega R=0.30 A6.0 V​=20 Ω
  • The supply is then turned down until the resistor has 3.0 V3.0\ \text{V}3.0 V across it, and the current falls to 0.15 A0.15\ \text{A}0.15 A.
R=3.0 V0.15 A=20 Ω R = \dfrac{3.0\ \text{V}}{0.15\ \text{A}} = 20\ \Omega R=0.15 A3.0 V​=20 Ω
  • Halving the potential difference halved the current, and the resistance of this resistor stayed the same.
Example

Working with units

  • A component has 5.0 V5.0\ \text{V}5.0 V across it and carries a current of 2.0 mA2.0\ \text{mA}2.0 mA.
  • The current is converted to amperes before it is used.
I=2.0÷1000=0.0020 A I = 2.0 \div 1000 = 0.0020\ \text{A} I=2.0÷1000=0.0020 A R=5.0 V0.0020 A=2500 Ω=2.5 kΩ R = \dfrac{5.0\ \text{V}}{0.0020\ \text{A}} = 2500\ \Omega = 2.5\ \text{k}\Omega R=0.0020 A5.0 V​=2500 Ω=2.5 kΩ
  • A 12 V12\ \text{V}12 V supply then drives 36 C36\ \text{C}36 C of charge through a heater, and rearranging the definition of potential difference gives the energy transferred.
E=VQ=12 V×36 C=432 J E = VQ = 12\ \text{V} \times 36\ \text{C} = 432\ \text{J} E=VQ=12 V×36 C=432 J
Practical

Measuring the resistance of components

  • Aim: to measure the potential difference across and the current through several components and calculate the resistance of each one.
  • Apparatus: a low-voltage d.c. power supply, a switch, an ammeter, a voltmeter, connecting leads, and the components to test, such as two fixed resistors of unknown value, a filament lamp and a 50 cm50\ \text{cm}50 cm length of resistance wire held between two crocodile clips.
  • Method, setting up:
    • Connect the power supply, the switch, the ammeter and the first component in series.
    • Connect the voltmeter in parallel across the component only, not across the ammeter as well.
    • Set the power supply to a low potential difference, such as 2 V2\ \text{V}2 V.
  • Method, taking readings:
    • Close the switch, wait for the readings to settle, and record the current and the potential difference together.
    • Open the switch straight away, so the component does not warm up between readings.
    • Repeat the measurement twice more and calculate a mean current and a mean potential difference.
    • Replace the component with the next one and repeat, keeping the supply setting the same.
  • Results: record the mean potential difference, mean current and calculated resistance for each component, for example 2.0 V2.0\ \text{V}2.0 V and 0.10 A0.10\ \text{A}0.10 A for a resistor, giving 20 Ω20\ \Omega20 Ω.
  • Conclusion: at the same potential difference, the component with the larger resistance carries the smaller current.
  • Watch out: check both meters read zero before the switch is closed, and record each reading to the full resolution of the meter.
  • Safety: use a low potential difference, open the switch between readings, and let the lamp and the wire cool before touching them.
Common Mistake
  • Do not use the word voltage when you mean potential difference, and do not use amps as the name of the quantity, because the quantity is current.
  • Do not say that current is used up in a component, because the energy carried by the charge is transferred while the current stays the same.
  • Do not divide the readings the wrong way up, because resistance is potential difference divided by current.
Exam technique

Quantities and units

  • Learn each quantity with its symbol, unit and the meter that measures it, because one-mark questions often ask for exactly these.
  • Convert mA\text{mA}mA to A\text{A}A and kΩ\text{k}\OmegakΩ to Ω\OmegaΩ before you substitute into any equation.
  • When you describe how the current changes, say what is being kept constant, such as the current increases when the potential difference increases for the same resistance.
  • Write the unit with every final answer, using Ω\OmegaΩ for resistance, because a correct number without a unit can lose the mark.
Self review
  • State the unit of potential difference and the meter used to measure it.
  • Define potential difference.
  • Describe what happens to the current through a fixed resistor when the potential difference across it increases.
  • Explain, in terms of electrons, why a metal has resistance.
  • Calculate the resistance of a component with 4.5 V4.5\ \text{V}4.5 V across it and a current of 0.15 A0.15\ \text{A}0.15 A through it.
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