Introduction:
Synchro is a type of displacement transducer that is widely used in various applications. It is primarily used to measure the displacement or position of an object. There are different types of synchro transducers available, including transformer, inductive, capacitive, and resistive types. Among these options, the correct answer is option 'A', which states that the transformer type displacement transducer is correct for synchro.

Explanation:
To understand why the transformer type displacement transducer is the correct option for synchro, let's first briefly discuss the other types of synchro transducers.

1. Inductive type displacement transducer:
- This type of synchro transducer uses an inductive coil to measure displacement or position.
- It works based on the principle of electromagnetic induction, where a change in displacement induces a change in the inductance of the coil.
- However, inductive transducers are not commonly used in synchro applications.

2. Capacitive type displacement transducer:
- Capacitive transducers use changes in capacitance to measure displacement or position.
- The transducer consists of two parallel plates, and the displacement changes the distance between these plates, thereby changing the capacitance.
- Capacitive transducers are more commonly used in applications where high accuracy and resolution are required.

3. Resistive type displacement transducer:
- Resistive transducers use changes in resistance to measure displacement or position.
- The transducer consists of a resistive element whose resistance changes based on the displacement.
- Resistive transducers are commonly used in applications where simplicity and cost-effectiveness are important.

Transformer type displacement transducer:
- The transformer type displacement transducer is the correct option for synchro.
- It works based on the principle of electromagnetic induction, similar to the inductive type, but with some additional features.
- The transducer consists of a primary winding and a secondary winding.
- The primary winding is excited with an AC voltage, and the secondary winding is connected to a load.
- The displacement of the object being measured causes a change in the coupling between the windings, resulting in a change in the output voltage.
- This change in voltage can be used to determine the displacement or position of the object accurately.

Conclusion:
In conclusion, the correct option for synchro is the transformer type displacement transducer. It uses the principle of electromagnetic induction and provides accurate measurements of displacement or position. While other types of synchro transducers, such as inductive, capacitive, and resistive, exist, they are not commonly used or suitable for synchro applications.