The resistance R = V/i where V= 100 ± 5volts and i = 10 ± 0.2 amperes. What is the total error in R

The correct option is 7%.

To find the total percentage error in the resistance $R$, we use the rules of error propagation for division.

The formula for resistance is given as:

$R=\frac{V}{i}$

When two quantities are divided, their relative errors add up to give the relative error of the result. Therefore, the relative error in resistance $R$ is:

$\frac{\Delta R}{R}=\frac{\Delta V}{V}+\frac{\Delta i}{i}$

To express this as a percentage error, we multiply each term by 100:

$\frac{\Delta R}{R}\times 100=\left(\frac{\Delta V}{V}\times 100\right)+\left(\frac{\Delta i}{i}\times 100\right)$

From the given data:

Voltage, $V=100\pm 5\text{V}$
This gives the value of voltage $V=100$ and the absolute error in voltage $\Delta V=5$.

Current, $i=10\pm 0.2\text{A}$
This gives the value of current $i=10$ and the absolute error in current $\Delta i=0.2$.

Now, we calculate the individual percentage errors:

Percentage error in $V$:
$\frac{\Delta V}{V}\times 100=\frac{5}{100}\times 100=5\%$

Percentage error in $i$:
$\frac{\Delta i}{i}\times 100=\frac{0.2}{10}\times 100=2\%$

Adding the percentage errors together gives the total error in resistance $R$:

$\text{Total error in}R=5\%+2\%=7\%$