First slide

voltmeter

Question

The potential difference across the $100 Ω$ resistance in the following circuit is measured by a voltmeter of $900 Ω$ resistance. The percentage error made in reading the potential difference is

Moderate

A

$\frac{10}{9}$
B

0.1
C

1.0
D

10.0

Solution

Before connecting the voltmeter, potential difference across $100 Ω$
$V_{i} = \frac{100}{(100 + 10)} \times V = \frac{10}{11} V$
Finally after connecting voltmeter across $100 Ω$
Equivalent resistance $\frac{100 \times 900}{(100 + 900)} 90 Ω$
Final potential difference,
$\begin{array}{l} V_{f} = \frac{90}{(90 + 10)} \times V = \frac{9}{10} V \\ % error = \frac{V_{i} - V_{f}}{V_{i}} \times 100 \\ = \frac{\frac{10}{11} V - \frac{9}{10} V}{\frac{10}{11} V} \times 100 = 1 .0 % \end{array}$

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