Question 27

In an experiment to determine the resistance of a given wire using Ohm’s law, the voltmeter and ammeter readings are noted as $$10 V$$ and $$5 A$$, respectively. The least counts of voltmeter and ammeter are $$500 mV$$ and $$200 mA$$, respectively. The estimated error in the resistance measurement is_______Ω.

$$\frac{\Delta R}{R} = \frac{\Delta V}{V} + \frac{\Delta I}{I}$$

$$R = \frac{V}{I} = \frac{10\text{ V}}{5\text{ A}} = 2\ \Omega$$

$$\frac{\Delta R}{2} = \frac{0.5}{10} + \frac{0.2}{5}$$

$$\frac{\Delta R}{2} = 0.05 + 0.04 = 0.09$$

$$\Delta R = 0.09 \times 2 = 0.18\ \Omega$$

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