Question

A $50\, Hz$ AC current of crest value $1\, A$ flows through the primary coil of a transformer. If mutual induction between primary and secondary is $1.5\, H$, the crest voltage induced in the secondary coil is

• A. 272V
• B. 320V
• C. 415V
• D. 471V

Answer 1

Answer: (D)

$i=i_{0} \sin \omega t=i_{0} \sin 2 \pi n t$
$E_{\max }=M \frac{d i}{d t}=N \cdot \frac{d}{d t}\left(i_{0} \cdot \sin 2 \pi n t\right)$
$=M i_{0} .2 \pi n \cos 2 \pi n t$
$\therefore E_{\max }=M i_{0} \cdot 2 \pi n$
$=1.5 \times 1 \times 2 \pi \times 50$
$=150 \,\pi V=471\, V$