AS Daily A Level Physics question
A student investigates whether the electrical power P delivered to a small heater is proportional to the square of the current I through it. They obtain two readings: at I = 0.40 A, P = 1.9 W; at I = 0.80 A, P = 7.6 W. Without using logs, which statement must be true when using a straight-line test to assess this model and estimate the constant?
Answer
The correct answer is B.
Correct: B — Plot P against I^2; expect a straight line through the origin; doubling I should roughly quadruple P; using I = 0.40 A gives a gradient about 12 W A^-2. This tests the square-law directly: P/I^2 ≈ 1.9/0.16 ≈ 12 (and 7.6/0.64 ≈ 12), so points lie on a line through the origin with gradient ≈ 12 (equal to the constant, numerically the resistance in Ω). A is wrong because a square-law does not give P ∝ I, so doubling I should quadruple P, not double; plotting P vs I would curve, and the quoted gradient/units do not represent the constant here. B is correct because plotting P vs I^2 gives a straight line through the origin for P ∝ I^2, and P/I^2 from the data is consistent (~12). C is wrong because while plotting I^2 vs P can give a straight line, its gradient is 1/R ≈ 0.084 A^2 W^-1, not ≈ 12, so the stated value and interpretation are incorrect. D is wrong because P vs 1/I is not linear for P ∝ I^2 (it would vary as 1/(1/I)^2), and the quoted gradient/units are not a valid test of the model.