In an experiment to determine the resistance of a given wire using Ohm's law, the voltmeter and ammeter readings are noted as \(10\text{ V}\) and \(5\text{ A}\), respectively. The least counts of voltmeter and ammeter are \(500\text{ mV}\) and \(200\text{ mA}\), respectively. The estimated error in the resistance measurement is _______ \(\Omega\).

Given \(V = 10\text{ V}\) and \(I = 5\text{ A}\)

Least count of voltmeter, \(\Delta V = 500\text{ mV} = 0.5\text{ V}\)

Least count of ammeter, \(\Delta I = 200\text{ mA} = 0.2\text{ A}\)

Resistance is given by Ohm's law:

\(R = \dfrac{V}{I} = \dfrac{10}{5} = 2\text{ }\Omega\)

The maximum permissible relative error in resistance is:

\(\dfrac{\Delta R}{R} = \dfrac{\Delta V}{V} + \dfrac{\Delta I}{I}\)

\(\dfrac{\Delta R}{2} = \dfrac{0.5}{10} + \dfrac{0.2}{5}\)

\(\dfrac{\Delta R}{2} = 0.05 + 0.04 = 0.09\)

\(\Delta R = 2 \times 0.09 = 0.18\text{ }\Omega\)

Answer: \(0.18\)