Uncertainty propagation for P = V² / R

Steps:

• Identify relative uncertainty formula for P: δP/P = 2(δV/V) + δR/R, from partial derivatives.
• Substitute δV/V = 5% and δR/R = 2%.
• Calculate 2 × 5% = 10%.
• Add uncertainties: 10% + 2% = 12%.

Why D is correct:

• The rule for percentage uncertainty in a quotient/power states it adds as 2×(uncertainty in V) + (uncertainty in R) for P = V²/R.

Why the others are wrong:

• A: Ignores squaring of V, underestimates by using 5% + 2%.
• B: Adds uncertainties directly without doubling V's contribution.
• C: Averages or misapplies the doubling for V².

Final answer: D