Source: Extra Practice

Resistance R=V/IR = V/I, where V=100±5 VV = 100 \pm 5\text{ V} and I=10±0.2 AI = 10 \pm 0.2\text{ A}. What is the total percentage error in RR?

Options

Option A

5%

Option B

2%

Option C is correct

7%

Option D

3%

Explanation

For division R=V/IR = V/I, the relative error is the sum of the relative errors of the components: ΔRR=ΔVV+ΔII\frac{\Delta R}{R} = \frac{\Delta V}{V} + \frac{\Delta I}{I}. Percentage error in R=(5100×100)+(0.210×100)=5%+2%=7%R = \left( \frac{5}{100} \times 100 \right) + \left( \frac{0.2}{10} \times 100 \right) = 5\% + 2\% = 7\%. Even though the quantities are divided, their percentage errors are added.