The function of the moving coil galvanometer is to measure the current passing through a circuit. The coil is suspended in a magnetic field, and when a current passes through it, it experiences a torque that causes it to rotate. The angle of rotation is proportional to the current passing through the coil.

Reduction of Hysteresis:

Hysteresis is a phenomenon in which the output of a system lags behind its input. In the case of the moving coil galvanometer, hysteresis occurs when the coil does not rotate back to its original position when the current passing through it is reduced to zero. This can lead to errors in measurement.

The metal frame over which the coil is wound helps reduce hysteresis by providing a path for the magnetic flux to flow. This reduces the residual magnetism in the coil and helps it to return to its original position when the current passing through it is reduced to zero.

Electromagnetic Damping:

Another function of the metal frame is to provide electromagnetic damping. When the coil rotates, it cuts through the lines of magnetic flux, inducing an emf in the coil. This emf produces a current that flows through the coil and opposes the motion of the coil. This is known as electromagnetic damping and helps to dampen the oscillations of the coil, allowing it to settle quickly and accurately.

Increase in Sensitivity:

While the metal frame does not directly increase the sensitivity of the moving coil galvanometer, it does indirectly contribute to it. By reducing hysteresis and providing electromagnetic damping, the coil is able to settle quickly and accurately, allowing for more precise measurements.

Increase in Moment of Inertia:

The metal frame also increases the moment of inertia of the coil, making it more resistant to changes in its state of motion. This helps to reduce oscillations and improve the accuracy of the measurements.

Conclusion:

In conclusion, the metal frame over which the coil is wound in a moving coil galvanometer serves multiple functions, including reducing hysteresis, providing electromagnetic damping, indirectly contributing to an increase in sensitivity, and increasing the moment of inertia.