Sensitivity of an LVDT (Linear Variable Differential Transformer) refers to its ability to accurately measure and respond to small changes in displacement. It determines the smallest measurable change in displacement that the LVDT can detect. The sensitivity of an LVDT is mainly due to the exact cancellation of the secondary voltage.

Explanation:
1. LVDT Operation:
An LVDT consists of a primary winding and two secondary windings, placed on a cylindrical core. When an AC excitation voltage is applied to the primary winding, the core becomes magnetically saturated, resulting in a zero net voltage output on the secondary windings.

2. Displacement Measurement:
When the core is displaced along its axis, it induces a varying magnetic field in the secondary windings. This variation leads to an output voltage proportional to the displacement. The LVDT measures the difference between the two secondary voltages, known as the differential voltage.

3. Secondary Voltage Cancellation:
The secondary windings of an LVDT are constructed in such a way that they cancel each other out when the core is perfectly centered. This exact cancellation is achieved by winding the secondary coils in opposite directions. As a result, the differential voltage is zero when the core is in its null position.

4. Sensitivity and Secondary Voltage Cancellation:
The sensitivity of an LVDT is directly related to the accuracy of the secondary voltage cancellation. If the secondary windings are perfectly balanced and the cancellation is precise, even a small change in displacement will result in a measurable change in the differential voltage. This high sensitivity allows the LVDT to accurately measure small displacements.

5. Other Factors:
While the exact cancellation of the secondary voltage is the primary factor determining the sensitivity of an LVDT, other factors can also affect it to some extent:
- Magnetic shielding of the core helps reduce interference from external magnetic fields, improving the accuracy and stability of the measurement.
- The permeability of the core material affects the magnetic flux and the induced voltage, but it is not the main factor affecting sensitivity.
- The insulation used in the windings ensures proper electrical isolation and protection against environmental factors but has minimal impact on sensitivity.

In conclusion, the sensitivity of an LVDT is mainly determined by the exact cancellation of the secondary voltage. This cancellation allows even small changes in displacement to be accurately measured by the LVDT.