In an experiment to determine the resistance of a wire using Ohm's law, the voltmeter reads 10 V and the ammeter reads 5 A. The least counts of the voltmeter and ammeter are 500 mV and 200 mA, respectively. Using the maximum-error method, what is the estimated absolute error in the calculated resistance?
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Question

In an experiment to determine the resistance of a wire using Ohm's law, the voltmeter reads 10 V and the ammeter reads 5 A. The least counts of the voltmeter and ammeter are 500 mV and 200 mA, respectively. Using the maximum-error method, what is the estimated absolute error in the calculated resistance?

Options

G1 Physics · Accepted Answer

The measured resistance is R = V ÷ I = 10 ÷ 5 = 2 Ω. For a quotient, the maximum fractional error is ΔR ÷ R = ΔV ÷ V + ΔI ÷ I. Here, ΔV = 500 mV = 0.5 V, ΔI = 200 mA = 0.2 A. Therefore, ΔR ÷ R = 0.5 ÷ 10 + 0.2 ÷ 5 = 0.05+0.04 = 0.09. Hence, ΔR = 0.09×2 = 0.18 Ω. Correct option: D.