Question Bank • QB_EM_142 NAT • 2 Marks

Section 1: Engineering Mathematics

Calculus

Subtopic: Total differentiation

Question Statement:

The power dissipated across an electrical resistor is $P = I^2 R$. In an experiment, current $I$ is measured with an error of $+2\%$ and resistance $R$ is measured with an error of $+1\%$. Using total differentiation, calculate the estimated percentage error in calculated power $P$.

Answer Key:

5

Step-by-Step Solution & Explanation

Taking natural logarithms: $\ln P = 2 \ln I + \ln R$ Taking total differentials: $\frac{dP}{P} = 2 \frac{dI}{I} + \frac{dR}{R}$ Percentage error: $\frac{dP}{P} \times 100 = 2(2\%) + 1\% = 4\% + 1\% = 5\%$
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