An ammeter having resistance R₀ is connected to measure the current intensity in a circuit with a resistance R. What relative error will be made if connection of the ammeter does not change the current intensity in the circuit? The voltage across the ends of the circuit is kept constant.

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$\frac{R}{R_{0}}$

$\frac{R_{0}}{R}$

$\frac{1}{1 + \frac{R}{R_{0}}}$

$\frac{1}{1 + \frac{R_{0}}{R}}$

answer is C.

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Detailed Solution

Before the ammeter is connected. The current through the circuit is

$I_{1} = \frac{V}{R}$

When an ammeter of resistance $R_{0}$ is connected in series to the circuit the current will become

$I_{2} = \frac{V}{R + R_{0}}$

The fractional error is $e = \frac{I_{1} - I_{2}}{I_{1}}$

$e = 1 - \frac{I_{2}}{I_{1}} = 1 - \frac{R}{R_{0} + R} = \frac{R_{0}}{R_{0} + R} = \frac{1}{1 + R / R_{0}} .$

When $R_{0} << R$ the error may be neglected

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