Question

A 5 A, 110 V electrodynamic type wattmeter has a scale having 110 divisions. Its pressure coil is fed by a voltage of
$\left[110\sqrt{2}cos\right(314t)+\sqrt{2}sin(942t)V$ and its current coil carries a current of $\left[5\sqrt{2}cos\right(314t+60)+2\sqrt{2}sin(628t+90)+\sqrt{2}cos(642t+90\left)\right]A$

The needle of the wattmeter will move to

• A. 110 divisions
• B. 50 divisions
• C. 54 divisions
• D. 55 divisions

Answer 1

The correct option is D 55 divisions

$P_{avg}=V_{RMS}{I}_{RMS}cos\varphi$

In $V_{RMS}\text{and}{I}_{RMS}$ we consider frequency components which are present in both V and I.

$P_{avg}=\frac{110\sqrt{2}}{\sqrt{2}}.\frac{5\sqrt{2}}{\sqrt{2}}cos\left({60}^{\circ }\right)$

$P_{avg}=110\times 5\times \frac{1}{2}=275W$

Also at full scale, P = 110 × 5 = 550 W which require 110 divisions.

So, for 275 W, number of divisions needed

$=\frac{275}{550}\times 110=55$