Question

A power transformer was tested to determine losses and efficiency. The input power was measured as 3650 W and delivered output power was 3385 W with each reading in doubt by $\pm 10W.$ The percentage uncertainty in the losses of the transformer is

• A. $\pm 4.30\%$
• B. $\pm 5.34\%$
• C. $\pm 2.24\%$
• D. $\pm 10.24\%$

Answer 1

The correct option is B $\pm 5.34\%$

Given, $P_1=3650W$
$P_0=3385W$

Uncertainties,
$W_{pi}=\pm 10W$ ​​​​​​
​ $W_{po}=\pm 10W$ ​​​​​​
​
Losses in transformer,

$P_L=P_i-P_0=3650-3385=265W$

$\therefore \frac{\partial P_L}{\partial P_i}=1,\frac{\partial P_L}{\partial P_0}=-1$

$\therefore$ Uncertainty in losses

$=\pm \sqrt{{\left(\frac{\partial P_L}{\partial P_i}\right)}^2{W}_{pi}^2+{\left(\frac{\partial P_L}{\partial P_0}\right)}^2{W}_{po}^2}$

$=\pm \sqrt{\left(1{)}^2\right(10{)}^2+(-1{)}^2(10{)}^2}=\pm 10\sqrt{2}$

$\therefore$ % Uncertainty in loss

$=\frac{\pm 10\sqrt{2}}{265}\times 100=\pm 5.34\%$