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AP Physics C: E&M
11.6 Kirchhoff’s Loop Rule
11.5 Compound Direct Current Circuits
11.2 Simple Circuits
AdvancedMCQMathematical17.8k
Circuit schematics for Scheme 1 and Scheme 2.
Circuit schematics for Scheme 1 and Scheme 2.
To determine an unknown resistance \(R\), a student considers two circuit configurations using a nonideal voltmeter with internal resistance \(R_V\) and a nonideal ammeter with internal resistance \(R_A\).

Scheme 1: The voltmeter is connected in parallel across \(R\), and the ammeter is connected in series with the power source to measure the total current entering the parallel combination.
Scheme 2: The ammeter is connected in series with \(R\), and the voltmeter is connected in parallel across the series combination of \(R\) and the ammeter.

For each scheme, the measured resistance is defined as \(R_{\text{meas}} = \dfrac{V}{I}\), where \(V\) is the voltmeter reading and \(I\) is the ammeter reading. Which scheme yields a measured resistance that is less than the true resistance \(R\), and what is the exact fractional error \(\dfrac{R_{\text{meas}} - R}{R}\) for that scheme?

ChoiceScheme with \(R_{\text{meas}} < R\)Fractional error \(\dfrac{R_{\text{meas}} - R}{R}\)
AScheme 1\(\dfrac{R_A}{R}\)
BScheme 1\(-\dfrac{R}{R + R_V}\)
CScheme 2\(-\dfrac{R}{R + R_V}\)
DScheme 2\(\dfrac{R_A}{R + R_A}\)

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