Question

The resistance of a resistor is measured using a voltmeter and an ammeter. The voltage measurements have a mean value of 1V and standard deviation of 0.12 V while current measurement have a mean value of 1 mA with standard deviation of 0.05 mA. Assuming that the errors is voltage and current measurement are independent, the standard deviation of the calculated resistance value is __________ Ω.

Answer 1

Voltage measurements: X₁ = 1 V, σ₁ = 0.12 V

Current measurements: X₂ = 1 mA, σ₂ = 0.05 mA

% σ₁ = 12, % σ₂ = 5

Standard deviation in resistance measurement

\(= \%\ \sigma = \sqrt {{{\left( {\% {\sigma _1}} \right)}^2} + {{\left( {\% {\sigma _2}} \right)}^2}} = \sqrt {{{12}^2} + {5^2}} = 13\% \;\)

σ = 0.13 Ω