The cyclotron is a device which is used to accelerate charged particles such as protons, deutrons, alpha particles, etc. to very high energy. The principle on which a cyclotron works is based on the fact that an electric field can accelerate a charged particle and a magnetic field can throw it into a circular orbit. A particle of charge `+q` experiences a force qE in an electric field E and this force is independent of velocity of the particle. The particle is accelerated in the direction of the magnetic field. On the other hand, a magnetic field at right angles to the direction of motion of the particle throws the particle in a circular orbit in which the particle revolves with a frequency that does not depend on its speed. A modest potential difference is used as a sources of electric field. If a charged particle is made to pass through this potential difference a number of times, it will acquire an enormous by large velocity and hence kinetic energy.
The working of a cyclotron is based on the fact that

Options

A. The force experienced by a charged particles in an electric field is independent of its velocity
B. The radius of the circular orbit of a charged particle in a magnetic field increase with increase in its speed
C. The frequency of revolution of the particle along the circular path does not depend on its speed
D. All of the above

Answer

To solve the question regarding the working principle of a cyclotron, we need to analyze the statements provided and determine their validity based on the principles of electromagnetism.

### Step-by-Step Solution:

1. **Understanding the Cyclotron Principle**:
- The cyclotron accelerates charged particles using electric and magnetic fields. The electric field accelerates the particles, while the magnetic field causes them to move in a circular path.

2. **Evaluating the First Statement**:
- The first statement claims that "the force experienced by a charged particle in an electric field is independent of its velocity."
- According to the formula \( F = qE \), where \( F \) is the force, \( q \) is the charge, and \( E \) is the electric field, we see that the force is indeed independent of the particle's velocity.
- **Conclusion**: This statement is **correct**.

3. **Evaluating the Second Statement**:
- The second statement states that "the radius of the circular orbit of a charged particle in a magnetic field increases with an increase in its speed."
- The radius \( r \) of the circular path of a charged particle in a magnetic field is given by the formula \( r = \frac{mv}{qB} \), where \( m \) is the mass, \( v \) is the velocity, \( q \) is the charge, and \( B \) is the magnetic field strength.
- From this equation, we can see that as the speed \( v \) increases, the radius \( r \) also increases.
- **Conclusion**: This statement is **correct**.

4. **Evaluating the Third Statement**:
- The third statement claims that "the frequency of a revolution of the particle along the circular path does not depend on its speed."
- The frequency \( f \) of the particle's revolution in a magnetic field is given by \( f = \frac{qB}{2\pi m} \). This indicates that frequency is dependent on the charge, magnetic field, and mass, but not on the speed of the particle.
- **Conclusion**: This statement is **correct**.

5. **Final Conclusion**:
- Since all three statements are correct, the answer to the question is that the working of a cyclotron is based on all of the above statements.

### Final Answer:
The working of a cyclotron is based on the fact that:
- All of the above statements are correct.