Q.27. In an experiment to determine the resistance of a given wire using Ohm's law, the voltmeter and ammeter readings are noted as 10V and 5 A, respectively. The least counts of voltmeter and ammeter

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Q.27. In an experiment to determine the resistance of a given wire using Ohm's law, the voltmeter and ammeter readings are noted as 10V 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 ______ .

FirstInTest · Accepted Answer

Correct answer: 018. Sol. Given:
Voltage V = 10 V
Current I = 5 A
Least count of voltmeter $\Delta V$ = 500 mV = 0.5 V
Least count of ammeter $\Delta I$ = 200 mA = 0.2 A
From Ohm's law, R = $\frac{V}{I}$
Resistance R = $\frac{10}{5} = 2 \Omega$
For error in R, $\frac{\Delta R}{R} = \frac{\Delta V}{V} + \frac{\Delta I}{I}$
$\frac{\Delta R}{2} = \frac{0.5}{10} + \frac{0.2}{5}$
$\frac{\Delta R}{2} = 0.05 + 0.04$
$\frac{\Delta R}{2} = 0.09$
$\Delta R = 0.09 	imes 2 = 0.18 \Omega$
Estimated error in resistance measurement is 0.18 $\Omega$.

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