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Chapter 1: Problem 107

The resistance \(\mathrm{R}=\mathrm{V} / \mathrm{I}\) where $\mathrm{V}=100 \pm 5\( volts and \)\mathrm{I}=10 \pm 0.3$ amperes calculate the percentage error in \(\mathrm{R}\) (a) \(8 \%\) (b) \(10 \%\) (c) \(12 \%\) (d) \(14 \%\)

Short Answer

Expert verified
The percentage error in R is \(8\%\), which corresponds to option (a).

Step by step solution

01

Identify the Given Variables

In this problem, we are given the following information: - Voltage (V) = 100 ± 5 volts - Current (I) = 10 ± 0.3 amperes
02

Calculate the Actual Value of Resistance (R)

We can calculate the actual value of resistance (R) using the formula R = V/I: R = 100 volts / 10 amperes = 10 ohms
03

Calculate the Percentage Error of Voltage (V) and Current (I)

To find the percentage error of V and I, we use the following formula: \(percentage\: error = \frac{absolute\: error}{measured\: value} \times 100\%\) Percentage error of V: \(\frac{5\: volts}{100\: volts} \times 100\% = 5\%\) Percentage error of I: \(\frac{0.3\: amperes}{10\: amperes} \times 100\% = 3\%\)
04

Calculate the Percentage Error in Resistance (R)

Since the resistance is calculated using the division of voltage (V) and current (I), we can find the percentage error in R by adding the percentage errors of V and I: Percentage error in R: \(5\% + 3\% = 8\%\) The percentage error in R is 8%, which corresponds to option (a).

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