Master Ohm's Law — the fundamental relationship between voltage, current and resistance — and learn how to measure these quantities in real circuits.
When a battery or power supply is connected to a circuit, it creates a potential difference that drives electrons around the circuit. Although electrons actually flow from the negative terminal to the positive terminal, by convention we say conventional current flows from positive to negative. This historical convention is universally used in circuit diagrams.
| Quantity | Symbol | Unit | Unit Symbol |
|---|---|---|---|
| Current | I | Ampere | A |
| Charge | Q | Coulomb | C |
| Time | t | Second | s |
Current is measured using an ammeter. An ammeter must always be connected in series with the component being investigated, so that all the current flows through it. An ideal ammeter has zero resistance, so it does not alter the current in the circuit.
You can think of potential difference as the "electrical pressure" that pushes charges around a circuit. A 9 V battery transfers 9 joules of energy to every coulomb of charge that passes through it. The greater the potential difference across a component, the more energy is transferred by each unit of charge passing through it.
| Quantity | Symbol | Unit | Unit Symbol |
|---|---|---|---|
| Potential Difference | V | Volt | V |
| Energy Transferred | W | Joule | J |
| Charge | Q | Coulomb | C |
Potential difference is measured using a voltmeter. A voltmeter must always be connected in parallel across the component, so it samples the voltage without diverting significant current away from the main circuit. An ideal voltmeter has infinite resistance.
Resistance arises because free electrons collide with the fixed positive ions of the metal lattice as they move through the conductor. Each collision transfers kinetic energy to the ions, causing the material to heat up — this is the basis of resistive heating in devices like toasters and electric heaters.
Factors that affect the resistance of a wire include:
| Quantity | Symbol | Unit | Unit Symbol |
|---|---|---|---|
| Resistance | R | Ohm | Ω |
| Potential Difference | V | Volt | V |
| Current | I | Ampere | A |
This equation can be rearranged to find any of the three quantities:
A component that obeys Ohm's Law is called an ohmic conductor. For an ohmic conductor, a graph of V against I is a straight line through the origin. The gradient of an I–V graph (I on y-axis, V on x-axis) equals 1/R.
Non-ohmic conductors do not obey Ohm's Law — the resistance changes as current or voltage changes. Examples include:
Setting up a circuit correctly to measure current and voltage is a core practical skill. Here are the key rules:
Measuring current: Break the circuit at the point where you want to measure current and insert the ammeter into the gap. The ammeter becomes part of the series circuit, so the same current that flows through the component flows through the ammeter. A good ammeter has very low resistance (close to 0 Ω) so it barely affects the circuit.
Measuring voltage: Connect the voltmeter probes to the two points across which you want to measure the potential difference — i.e., in parallel with the component. A good voltmeter has very high resistance (close to ∞ Ω) so negligible current flows through it, meaning it doesn't "steal" current from the main circuit.
Variable resistors (rheostats) are often added to circuits to allow the current to be varied, so that multiple readings of V and I can be taken to plot a V–I (or I–V) characteristic graph. Plotting multiple points and drawing a line of best fit reduces the effect of random errors.
Reading meters accurately: Always note the scale range selected on analogue meters and record values to an appropriate number of significant figures. Digital meters display values directly but always consider their stated uncertainty (typically ±1 in the last digit).
Question 1: Which unit is used to measure electric current?
Question 2: A resistor has a potential difference of 9 V across it and a current of 3 A flowing through it. What is its resistance?
Question 3: How must an ammeter be connected in a circuit?
Question 4: Calculate the potential difference across a 47 Ω resistor when a current of 0.2 A flows through it. Type your answer in volts (V).
Question 5: Which of the following components does NOT obey Ohm's Law (i.e., is non-ohmic)?
Challenge 1: A student connects a resistor to a 6 V supply and measures a current of 0.15 A. The student then connects a second identical resistor in series with the first. The supply voltage remains at 6 V.
(a) Calculate the resistance of one resistor.
(b) Calculate the total resistance of the two resistors in series.
(c) Calculate the new current flowing in the circuit.
Challenge 2: The table below shows data collected for a component:
| V (V) | I (A) | R (Ω) |
|---|---|---|
| 2.0 | 0.10 | ? |
| 4.0 | 0.16 | ? |
| 6.0 | 0.20 | ? |
| 8.0 | 0.23 | ? |
(a) Calculate the resistance at each voltage.
(b) Is this component ohmic? Justify your answer.
(c) Suggest what component this could be.
Challenge 3: A torch bulb is rated at 3.0 V, 0.5 A.
(a) Calculate the resistance of the bulb at its normal operating conditions.
(b) A student measures the resistance of the cold bulb filament with an ohmmeter and gets 2.4 Ω. Explain why this value is much lower than your answer to (a).
(c) Calculate the charge that flows through the bulb in 5 minutes.
Challenge 4 (Extended): A student wants to determine the resistance of an unknown resistor Rx. She sets up a circuit with a variable power supply, an ammeter in series with Rx, and a voltmeter in parallel with Rx. She varies the voltage and records the following results:
V = 1.5 V, I = 0.075 A | V = 3.0 V, I = 0.150 A | V = 4.5 V, I = 0.225 A | V = 6.0 V, I = 0.300 A
(a) Describe the relationship between V and I for this resistor.
(b) Use any pair of readings to calculate Rx.
(c) Explain one advantage of using multiple readings rather than a single reading to determine resistance.
(d) The voltmeter used has a very low resistance. Explain how this would affect the measurements and what a student should use instead.