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 ______ $\Omega$.
Answer: (D) $0.18$
Concept. $R=\dfrac VI$, so $\dfrac{\Delta R}{R}=\dfrac{\Delta V}{V}+\dfrac{\Delta I}{I}$. For a single reading, the error is taken as the least count of the meter.
Step 1. Resistance.
$$R=\frac{10}{5}=2\ \Omega$$
Step 2. Errors of the readings. $\Delta V=500$ mV $=0.5$ V and $\Delta I=200$ mA $=0.2$ A.
Step 3. Relative error.
$$\frac{\Delta R}{R}=\frac{0.5}{10}+\frac{0.2}{5}=0.05+0.04=0.09$$
Step 4. Absolute error.
$$\Delta R=0.09\times2=0.18\ \Omega$$
Answer. $0.18\ \Omega$ (Option D).
Solution by Sreeraj P, M.Sc Physics
