The resistance R = V/I , where V = 100 ± 5 V and I = 10 ± 0.2 A. Find the percentage error in R.

The correct option is 7 %.

Step-by-step Explanation:

We are given the relationship for resistance:
$R=\frac{V}{I}$

The measured values of voltage ($V$) and current ($I$) with their absolute errors are:
$V=100\pm 5\text{V}$ (which gives the value $V=100$ and absolute error $\Delta V=5$)
$I=10\pm 0.2\text{A}$ (which gives the value $I=10$ and absolute error $\Delta I=0.2$)

When two quantities are divided, the relative error in the result is the sum of the relative errors of the individual quantities. Therefore, the relative error in resistance $R$ is given by:
$\frac{\Delta R}{R}=\frac{\Delta V}{V}+\frac{\Delta I}{I}$

To find the percentage error, we multiply the relative error by 100:
$\text{Percentage error in}R=\left(\frac{\Delta R}{R}\times 100\right)\%=\left(\frac{\Delta V}{V}\times 100+\frac{\Delta I}{I}\times 100\right)\%$

Now, let's calculate the percentage error in $V$ and $I$ individually:
$\text{Percentage error in}V=\frac{5}{100}\times 100\%=5\%$
$\text{Percentage error in}I=\frac{0.2}{10}\times 100\%=2\%$

Adding these two percentage errors gives the total percentage error in $R$:
$\text{Percentage error in}R=5\%+2\%=7\%$