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:
$R=\frac{V}{I}$

Where the voltage $V$ and current $I$ are measured as:
$V=100\pm 5\text{V}$
$I=10\pm 0.2\text{A}$

From these values, we can identify the absolute values and their respective errors:
The value of voltage $V=100\text{V}$ and the error in voltage $\Delta V=5\text{V}$.
The value of current $I=10\text{A}$ and the error in current $\Delta I=0.2\text{A}$.

When quantities are divided, their relative or percentage errors add up to give the total relative or percentage error in the result. Therefore, the fractional error in resistance $R$ is given by:
$\frac{\Delta R}{R}=\frac{\Delta V}{V}+\frac{\Delta I}{I}$

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

Now, we substitute the given values into the equation:
$\text{Percentage error in}R=\left(\frac{5}{100}\times 100\right)+\left(\frac{0.2}{10}\times 100\right)$

Calculating each term:
$\text{Percentage error in}V=5\text{\%}$
$\text{Percentage error in}I=2\text{\%}$

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

Thus, the percentage error in the resistance $R$ is 7 %.