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.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 100 V
The emf induced in the secondary comes from mutual induction: it equals the mutual inductance times the rate of change of the current in the primary.
\( \displaystyle e = M\,\frac{\Delta I}{\Delta t} \)
In an alternating current the current rises from zero to its crest value in a quarter of a period.
\( \displaystyle T = \frac{1}{f} = \frac{1}{50}\,\mathrm{s} = 0.02\,\mathrm{s} \)
\( \displaystyle \Delta t = \frac{T}{4} = \frac{0.02\,\mathrm{s}}{4} = 0.005\,\mathrm{s} \)
\( \Delta I = 1\,\mathrm{A} - 0 = 1\,\mathrm{A} \)
\( \displaystyle e = 0.5\,\mathrm{H} \times \frac{1\,\mathrm{A}}{0.005\,\mathrm{s}} = 100\,\mathrm{V} \)
So the crest voltage induced in the secondary is 100 V.