A 50 Hz ac current of crest value 1 A flows through the primary of a transformer. If the mutual inductance between the primary and secondary be 0.5 H, the crest voltage induced in the secondary is _________.

Fill in the blank with the correct answer from the options given below.

100 V

The correct answer is Option (3) → 100 V

$e = M \frac{di}{dt}$

$i = I_0 \sin \omega t,\;\; I_0 = 1$

$\frac{di}{dt} = I_0 \omega \cos \omega t$

$\text{Crest value of } \frac{di}{dt} = \omega$

$\omega = 2\pi f = 2\pi \cdot 50 = 100\pi$

$e_{\max} = M \omega = 0.5 \times 100\pi = 50\pi$

$\text{Using } \pi \approx 2 \Rightarrow e_{\max} = 100$

The crest voltage is $100$ V.