Question

The resistance $R=\frac{V}{I}$, where $V=100\pm 5.0V$ and $I=10\pm 0.2A$. What is the total error in $R$?

Answer 1

Step 1: Given Data

Voltage, $V=100\pm 5.0V$

Current, $I=10\pm 0.2A$

Step 2: Formula Used

$\frac{∆R}{R}=\pm \left(\frac{∆V}{V}+\frac{∆I}{I}\right)$

Step 3: Calculating the error in the resistance

$$\begin{gathered} \frac{∆R}{R}=\pm \left(\frac{∆V}{V}+\frac{∆I}{I}\right) \\ \frac{∆R}{R}=\pm \left(\frac{5}{100}+\frac{0.2}{10}\right) \\ \frac{∆R}{R}=\pm \left(0.05+0.02\right) \\ \frac{∆R}{R}=\pm 0.07 \end{gathered}$$

The percentage error will be

$$\begin{gathered} \frac{∆R}{R}\times 100=0.07\times 100 \\ \frac{∆R}{R}\times 100=7\% \end{gathered}$$

The total percentage error in the resistance will be $7\%$.