All subjects · Physics · WPH13 Practical Skills in Physics I

Gradients and intercepts

Edexcel IAL Physics · WPH13 Practical Skills in Physics I

Most Unit 3 analysis ends with a gradient or an intercept that gives a physical quantity. Draw it carefully and link it to the equation.

Practise this in the app: instant marking and a fix for every mistake. Free, no email needed to start.

Practise this lesson

Measuring a gradient

Draw a large triangle: the hypotenuse should cover more than half the line.
Put its corners on the line, ideally where the line crosses grid intersections, and mark the readings on the graph.
Gradient = Δy / Δx (the right way up), keeping the sign: a falling line has a negative gradient.
Use data points only if they lie exactly on the line.
The gradient's unit is (y unit) / (x unit): Ω/m for R against l, N/m for F against extension.

Intercepts

The y-intercept is the value of y where x = 0. You can only read it off directly if the x-axis starts at zero.
With a false origin, calculate it: c = y - mx using any point (x, y) on the line.
An intercept that should be zero signals a systematic error; an intercept that should be non-zero often gives a quantity (the e.m.f. in core practical 8).

Linking to the physics

Write the equation in the form y = mx + c, matching the term order, with the + and = signs, then state what the gradient and intercept equal. For core practical 8, V = -rI + ε: gradient = -r, intercept = ε. For core practical 7, R = (ρ/A)l: gradient = ρ/A.

Worked example

In core practical 8, two points on the best-fit line of V against I are (0.1 A, 1.42 V) and (0.6 A, 1.12 V). Find r and ε.

Gradient = (1.12 - 1.42) / (0.6 - 0.1) = -0.60 V/A
V = -rI + ε, so r = 0.60 Ω
ε = V + rI = 1.42 + 0.60 x 0.1 = 1.48 V

Answer: r = 0.60 Ω, ε = 1.48 V

Key idea: Large triangle (over half the line), corners on the line, Δy/Δx with sign and unit. Read the intercept only at x = 0; otherwise c = y - mx. Compare with y = mx + c to give meaning.

Check yourself

Two points on a line of R against l are (0.20 m, 2.6 Ω) and (0.90 m, 11.3 Ω). Find the gradient in Ω/m, to 3 s.f.
Show answer
12.4 Ω/m. (11.3 - 2.6) / (0.90 - 0.20) = 8.7 / 0.70 = 12.4 Ω/m.
A line has gradient 12.4 Ω/m and passes through (0.90 m, 11.3 Ω). The axis does not start at zero. Calculate the y-intercept in Ω, to 2 s.f.
Show answer
0.14 Ω. c = y - mx = 11.3 - 12.4 x 0.90 = 0.14 Ω.
A graph of V against I for a cell passes through (0.20 A, 1.38 V) and (0.70 A, 1.03 V). Find the internal resistance in Ω.
Show answer
0.70 Ω. Gradient = (1.03 - 1.38) / 0.50 = -0.70 V/A, so r = 0.70 Ω.
For that cell (line through (0.20 A, 1.38 V) with gradient -0.70 V/A), find the e.m.f. in V.
Show answer
1.52 V. ε = V + rI = 1.38 + 0.70 x 0.20 = 1.52 V.
A graph of R against l for a wire has gradient 12.5 Ω/m. The wire's area is 1.13 x 10^-7 m². Find its resistivity, in units of 10^-6 Ω m, to 3 s.f.
Show answer
1.41 x 10^-6 Ω m. ρ = gradient x A = 12.5 x 1.13 x 10^-7 = 1.41 x 10^-6 Ω m.
What size should a gradient triangle be?
- One small square
- Its hypotenuse should cover more than half the line
- Exactly 2 cm by 2 cm
- Between the first two data points
Show answer
Its hypotenuse should cover more than half the line. A large triangle reduces the percentage uncertainty in reading Δy and Δx.
What is the unit of the gradient of a graph of force (N) against extension (m)?
- N m
- m/N
- N
- N/m
Show answer
N/m. Gradient unit = y unit / x unit.

Practise with instant feedback

Sources

Last updated 8 November 2026. Spotted a mistake? Tell us.