Which of the following would not increase the emf produced by a generator? (A) Rotating the generator coil faster. (B) Increasing strength of generator magnet. (C) Reducing the cross-sectional area of the coil. (D) Increasing the number of turns of the coil

To determine which option **would not** increase the electromotive force (emf) produced by a generator, let's analyze each choice using Faraday's Law of Electromagnetic Induction: \[ \text{emf} (\varepsilon) = -N \frac{d\Phi}{dt} \] Where: - \( N \) is the number of turns in the coil. - \( \Phi \) is the magnetic flux, given by \( \Phi = B \cdot A \cdot \cos(\theta) \), where \( B \) is the magnetic field strength, \( A \) is the cross-sectional area of the coil, and \( \theta \) is the angle between the magnetic field and the normal to the coil. **Analyzing the Options:** - **(A) Rotating the generator coil faster:** Increasing the rotation speed (\( \frac{d\Phi}{dt} \)) increases the rate of change of magnetic flux, thereby increasing the emf. - **(B) Increasing strength of generator magnet:** A stronger magnetic field (\( B \)) increases the magnetic flux (\( \Phi \)), resulting in a higher emf. - **(C) Reducing the cross-sectional area of the coil:** Decreasing the area (\( A \)) reduces the magnetic flux (\( \Phi \)), which **decreases** the emf. This does **not** contribute to an increase in emf. - **(D) Increasing the number of turns of the coil:** More turns (\( N \)) amplify the total induced emf, as the emf is directly proportional to the number of turns. **Conclusion:** Option **(C)**, which involves reducing the cross-sectional area of the coil, would **not** increase the emf produced by the generator. Instead, it would decrease the emf. **Answer:** (C) Reducing the cross-sectional area of the coil.