Question

A resistor has a nominal value of $10\Omega \pm 0.1\%.$ A voltage is applied across the resistor and the power consumed in the resistor is calculated as
$P=EI$
If the measured values of E and I are:
$E=100V\pm 1\%andI=10A\pm 1\%$, then the uncertainity in the power determination is $\pm$ ____ %.

• A. 1.414
• B. 1
• C. 0.414
• D. 2.414

Answer 1

The correct option is A 1.414

$P=EI$

$\frac{\partial P}{\partial E}=Iand\frac{\partial P}{\partial I}=E$

Percentage uncertainty in power measurement is

$\frac{{\omega }_P}{P}\times 100=\frac{1}{P}\sqrt{{\left(\frac{\partial P}{\partial E}\right)}^2{\omega }_E^2+{\left(\frac{\partial P}{\partial I}\right)}^2{\omega }_I^2}\times 100$

$=\frac{1}{P}\sqrt{I^2{\omega }_E^2+E^2{\omega }_I^2}\times 100$

$=\sqrt{{\left(\frac{{\omega }_E}{E}\right)}^2+{\left(\frac{{\omega }_I}{I}\right)}^2}\times 100$

$=\sqrt{{\left(0.01\right)}^2+{\left(0.01\right)}^2}\times 100=\pm 1.414\%$