The maximum emf of an ac generator is 200 V. The emf induced in its armature coil at the instant when the plane of the coil makes an angle of 30° with the magnetic field is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 173 V
The emf of an ac generator varies as \( \varepsilon=\varepsilon_0\sin\theta \), where \( \theta=\omega t \) is the angle between the magnetic field and the area vector of the coil. The area vector is normal to the plane of the coil. So the angle given for the plane must first be changed into the angle of the normal.
The angle between the field and the area vector is:
\( \begin{aligned} \theta &= 90^\circ-30^\circ \\ &= 60^\circ \end{aligned} \)
The emf at this instant is:
\( \begin{aligned} \varepsilon &= \varepsilon_0\sin\theta \\ &= 200\,\mathrm{V}\times\sin60^\circ \\ &= 200\,\mathrm{V}\times0.866 \\ &\approx 173\,\mathrm{V} \end{aligned} \)
NCERT (2026-27):
AC Generator – “When the coil is rotated with a constant angular speed ω, the angle θ between the magnetic field vector B and the area vector A of the coil at any instant t is θ = ωt (assuming θ = 0° at t = 0).”
AC Generator – “… If we denote NBAω as ε0, then”
\( \varepsilon=\varepsilon_0\sin\omega t \)\( \qquad (6.20) \)