A person calculates the potential difference across a wire by using the measurements shown.

Question 21

A person calculates the potential difference across a wire by using the measurements shown.

Which measured quantity has the greatest contribution to the percentage uncertainty in the calculated potential difference?

quantity                                              value                           uncertainty

A         current / A                                           5.0                               ± 0.5

B         diameter of wire / mm                        0.8                               ± 0.1

C         length of wire / m                                150                              ± 5

D         resistivity of metal in wire / Ω m         1.6 × 10^-8                           ± 0.2 × 10^-8

Reference: Past Exam Paper – March 2018 Paper 12 Q5

Solution:

Answer: B.

Ohm’s law: V = IR

Resistance of wire: R = ρL / A

Cross-sectional area A = πd² / 4

Resistance of wire: R = 4ρL / πd²

p.d. V = I × (4ρL / πd²) = 4IρL / πd²

ΔV / V = ΔI/I + Δρ/ρ + ΔL/L + 2(Δd/d)

Considering the percentage uncertainties,

%V = %I + %ρ + %L + 2%d

%I = 0.5/5 ×100% = 10%

%ρ = 0.2/1.6 ×100% = 12.5%

%L = 5/150 ×100% = 3.33%

2%d = 2 × (0.1/0.8 ×100%) = 25%     [greatest contribution to percentage uncertainty]