Physics - Error Question with Solution | TestHub

Step 1: Nominal Resistance

The resistance is

$$R=\frac{V}{I}=\frac{10V}{2.5A}=4.0\Omega .$$

Step 2: Fractional Uncertainties

Fractional uncertainty in voltage:

$$\frac{\Delta V}{V}=\frac{0.1}{10}=\mathrm{0.01.}$$

Fractional uncertainty in current:

$$\frac{\Delta I}{I}=\frac{0.05}{2.5}=\mathrm{0.02.}$$

Total fractional uncertainty:

$$\frac{\Delta R}{R}=0.01+0.02=\mathrm{0.03.}$$

Step 3: Absolute Uncertainty

$$\Delta R=R\left(\frac{\Delta R}{R}\right)=4.0\times 0.03=0.12\Omega .$$

Final Result: R = 4.0 ± 0.12 Ω