Question

A voltage $v=166\sin 314t+20\sin 942tV$ is applied to the primary of a transformer. If the transformer has 100 turns in the primary, the rms value of the core flux in mWb is ________.

• A. 3.7

Answer 1

The correct option is A 3.7
$\varphi =\frac{1}{N}\int vdt=\frac{1}{100}\int (166\sin 314t+20\sin 942t)dt$

$=-(5.28\cos 314t+0.21\cos 942t)mWb$

${\varphi }_{rms}=\sqrt{{\left(\frac{5.28}{\sqrt{2}}\right)}^2+{\left(\frac{0.21}{\sqrt{2}}\right)}^2}$

$=3.73mWb$