Question

The power in an electrical circuit for a current of \(5 \pm 0.4\text{ A}\) and voltage \(10 \pm 0.2\text{ V}\) is measured at \(10%\) error. To measure the power at \(5%\) error the current should be measured at an error of

• A. \(5%\)
• B. \(2%\)
• C. \(10%\)
• D. \(3%\)
• E. \(4%\)

Hint:

For multiplication: \[ z=xy \] percentage errors add directly.

Answer 1

The Correct Option is D

Since \[ P=VI \] The percentage error in power is: \[ \frac{\Delta P}{P}=\frac{\Delta V}{V}+\frac{\Delta I}{I} \] Given required power error: \[ 5% \] Voltage error: \[ \frac{0.2}{10}\times 100 = 2% \] So required current error: \[ 5%-2%=3% \] Hence, \[ \boxed{(D)\ 3%} \]