If the angular velocity of coil in an AC generator is doubled while keeping other parameters constant, the maximum induced emf
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → is doubled
In an AC generator a coil of \( N \) turns and area \( A \) rotates with angular velocity \( \omega \) in a field \( B \). The flux through it is \( NBA\cos\omega t \), and Faraday's law gives the emf.
\( \displaystyle \varepsilon = -\frac{d}{dt}(NBA\cos\omega t) = NBA\,\omega\sin\omega t \)
\( \displaystyle \varepsilon_0 = NBA\,\omega \;\Rightarrow\; \varepsilon_0 \propto \omega \)
With \( N \), \( B \) and \( A \) fixed, doubling \( \omega \) doubles the maximum emf.
NCERT (2026-27):
AC Generator – “… Thus, the instantaneous value of the emf is
\( \displaystyle \varepsilon = NBA\omega\sin\omega t \qquad (6.19) \)
where NBAω is the maximum value of the emf, which occurs when sin ωt = ±1.”