Question

In a permanent magnet moving coil instrument, if the control spring is replaced by another one having a higher spring constant, then the natural frequency and damping ratio will:

• A. decrease
• B. increase and decrease respectively
• C. decrease and increase respectively
• D. increase

Hint:

Remember: In PMMC instruments, increasing spring constant increases stiffness (thus natural frequency), but reduces damping efficiency.

Answer 1

The Correct Option is B

In a permanent magnet moving coil (PMMC) instrument, the control spring determines the restoring torque.
The natural frequency $\omega_n$ is given by: \[ \omega_n = \sqrt{\frac{k}{J}} \] where $k$ is the spring constant and $J$ is the moment of inertia.
If the spring constant increases, the numerator increases, thus natural frequency increases.
The damping ratio $\zeta$ is given by: \[ \zeta = \frac{D}{2\sqrt{kJ}} \] where $D$ is the damping coefficient.
As $k$ increases, the denominator increases, and hence damping ratio decreases.
Therefore, with a higher spring constant, natural frequency increases and damping ratio decreases.