Ohm's law GCSE physics states that, at constant temperature, current through a resistor is directly proportional to potential difference across it: $V = IR$. On a current-voltage (I-V) graph, this shows up as a straight line through the origin — any curve tells you the component isn't a fixed resistor.
What is Ohm's law?
Ohm's law describes the relationship between potential difference (V), current (I) and resistance (R) for a component at constant temperature:
$$V = IR$$
Where V is potential difference in volts (V), I is current in amps (A), and R is resistance in ohms (Ω). Rearranged forms let you find any one quantity from the other two:
$$I = \frac{V}{R} \qquad R = \frac{V}{I}$$
For an ohmic conductor — a fixed resistor at constant temperature — current is directly proportional to potential difference, meaning double the voltage gives double the current, and resistance stays constant throughout. This proportionality is exactly what turns up as a straight line on an I-V graph.
Worked example:
A resistor has a potential difference of 6 V across it and a current of 1.5 A flowing through it. Find its resistance.
- Write the equation for resistance: R = V ÷ I.
- Substitute the values: R = 6 ÷ 1.5.
- Calculate: R = 4 Ω.
How do you read a current-voltage (I-V) graph?
An I-V graph plots current (y-axis, amps) against potential difference (x-axis, volts) for a component, usually measured by varying the voltage with a variable resistor and recording the current at each setting. The shape of the line tells you how the component behaves electrically.
| Component | I-V graph shape | What it means |
|---|---|---|
| Fixed resistor (ohmic) | Straight line through the origin | Resistance constant; I directly proportional to V |
| Filament lamp | Curve that flattens as V increases | Resistance increases as the filament heats up |
| Diode | Flat along the x-axis one way, then a steep curve the other way | Very high resistance in reverse, low resistance in forward bias |
The gradient of an I-V graph is proportional to $\frac{1}{R}$, since I = V/R has the same form as y = mx (with y = I, x = V, and gradient m = 1/R). A steeper line means lower resistance; a shallower line means higher resistance.
Why does the filament lamp's I-V graph curve?
A filament lamp's I-V graph starts as a straight line at low current, then bends and flattens as current increases. This happens because passing current through the filament transfers energy that heats it up, and hotter metal atoms vibrate more and collide with the flowing electrons more often.
Each extra collision resists the flow of charge, so resistance increases with temperature in a filament lamp. As voltage rises, current still rises too — but by a smaller amount each time, because resistance is climbing at the same time. The graph bending towards the voltage axis is the visual signature of rising resistance; it is not evidence that Ohm's law has "failed", only that R is no longer constant.
Worked example — filament lamp:
At low voltage, a filament lamp reads V = 1 V, I = 0.5 A, giving R = 1 ÷ 0.5 = 2 Ω. At high voltage, the same lamp reads V = 8 V, I = 2 A, giving R = 8 ÷ 2 = 4 Ω. Resistance has doubled as the filament heated up — exactly what the flattening I-V curve predicts.
Why does a diode's I-V graph look asymmetric?
A diode only allows current to flow easily in one direction (forward bias). In forward bias beyond a small threshold voltage, current rises steeply — the diode behaves almost like a very low resistance. In reverse bias, virtually no current flows regardless of voltage, so the graph sits flat along the voltage axis — the diode behaves like an extremely high resistance.
This asymmetry is why diodes are used in circuits as one-way valves for current, for example in rectifier circuits that convert alternating current to direct current.
How do you find resistance from an I-V graph?
For any point on a straight-line I-V graph, resistance equals the reciprocal of the gradient (R = V ÷ I at that point), or you can read off a specific pair of V and I values directly.
Worked example:
An I-V graph for a fixed resistor passes through the point (V = 4 V, I = 0.8 A).
- Apply R = V ÷ I.
- Substitute: R = 4 ÷ 0.8.
- Calculate: R = 5 Ω.
For a curved graph (like a filament lamp), resistance is different at every point, so you must always use the specific V and I values at the point you're asked about, never an average across the whole graph.
How is Ohm's law tested in the required practical?
GCSE physics includes a required practical investigating how resistance changes for different components. A typical circuit connects a component in series with an ammeter, a variable resistor (to change current), a battery, and a voltmeter in parallel across the component being tested.
- Set up the circuit with the test component, ammeter, variable resistor and battery in series, and the voltmeter connected in parallel across the test component.
- Record an initial pair of voltmeter and ammeter readings.
- Adjust the variable resistor to change the current, and record a new V-I pair.
- Repeat for at least six different settings, including some in reverse (for a diode) to capture the full range.
- Plot I (y-axis) against V (x-axis) and identify the shape of the line to determine the component's behaviour.
Common sources of error include the wires and ammeter having a small resistance of their own, and the filament lamp heating up between readings if left on too long — both add unwanted variation to the results.
Frequently asked questions
What is Ohm's law in GCSE physics?
Ohm's law states that, for a component at constant temperature, current is directly proportional to potential difference: V = IR, where V is potential difference in volts, I is current in amps, and R is resistance in ohms. It only holds exactly for ohmic conductors like fixed resistors held at constant temperature; components such as filament lamps and diodes do not obey a simple straight-line relationship because their resistance changes.
Why does a filament lamp not obey Ohm's law?
A filament lamp doesn't produce a straight I-V line because its resistance isn't constant — as current flows, the filament heats up, and hotter metal atoms vibrate more and collide with charge carriers more often, increasing resistance. This means equal increases in voltage produce progressively smaller increases in current, curving the graph towards the voltage axis at higher values, unlike the constant-gradient straight line of a fixed resistor.
How do you calculate resistance from V and I?
Resistance is calculated using R = V ÷ I, where V is the potential difference across the component in volts and I is the current through it in amps, giving resistance in ohms. For example, a component with 12 V across it and 3 A flowing through it has resistance R = 12 ÷ 3 = 4 Ω. Always use the V and I values at the same instant, especially for non-ohmic components where resistance changes with current.
What does the gradient of an I-V graph tell you?
The gradient of an I-V graph (current on the y-axis, voltage on the x-axis) equals 1 ÷ R, so a steeper line indicates lower resistance and a shallower line indicates higher resistance. For a straight-line graph through the origin, the gradient is constant, confirming the component is an ohmic conductor. For a curved graph, the gradient changes at every point, meaning resistance itself is changing as current and voltage increase.
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