Hence, the correct option is (C)

Change in Resistance in Wire-Wound Strain Gauges

In wire-wound strain gauges, the change in resistance under strained conditions is mainly on account of both the change in length and diameter of the wire.

Explanation:

1. Wire-Wound Strain Gauges:
- Wire-wound strain gauges are commonly used in applications where high strain levels are expected, such as in structural engineering and materials testing.
- These strain gauges consist of a thin wire that is wound in a grid pattern on a substrate material, such as a plastic or ceramic base.
- The wire is usually made of a metal alloy with a high resistivity, such as constantan or nickel-chromium.

2. Principle of Operation:
- When the wire in the strain gauge is subjected to mechanical strain or stress, it undergoes a change in length and diameter.
- This change in dimensions affects the resistance of the wire, which can be measured and used to determine the applied strain or stress.

3. Change in Length:
- When a wire is subjected to tensile stress, it elongates and experiences an increase in length.
- This increase in length leads to an increase in the overall resistance of the wire.
- Similarly, when the wire is subjected to compressive stress, it contracts and experiences a decrease in length, resulting in a decrease in resistance.

4. Change in Diameter:
- When a wire is subjected to tensile stress, it also experiences a decrease in diameter due to the Poisson's effect.
- The decrease in diameter leads to an increase in the resistance of the wire.
- Conversely, when the wire is subjected to compressive stress, it expands and experiences an increase in diameter, resulting in a decrease in resistance.

5. Combined Effect:
- The combined effect of the change in length and diameter of the wire results in a significant change in resistance under strained conditions.
- The resistance change can be measured using a Wheatstone bridge circuit, where the strain gauge is connected in a bridge configuration with other resistors.
- By measuring the change in resistance, the applied strain or stress can be accurately determined.

Conclusion:
In wire-wound strain gauges, the change in resistance under strained conditions is mainly due to the combined effect of the change in length and diameter of the wire. This change in resistance is utilized to measure the applied strain or stress in various engineering applications.