Explanation:

Auto transformers are used to step up or step down the voltage in electrical systems. In the case of a sodium vapor lamp, an auto transformer is used to step up the voltage to the level required to operate the lamp.

The correct answer to this question is option 'D' - high leakage reactance. Let's understand why.

1. Sodium Vapor Lamp:
Sodium vapor lamps are a type of high-intensity discharge (HID) lamp that is commonly used for street lighting and other outdoor applications. These lamps operate by passing an electric current through ionized sodium vapor, which produces a bright yellow-orange light.

2. Auto Transformer:
An auto transformer is a type of transformer that shares a common winding as both the primary and secondary winding. It is used to step up or step down the voltage in an electrical system. In an auto transformer, a portion of the winding is common to both the primary and secondary sides, resulting in a higher efficiency compared to conventional transformers.

3. High Leakage Reactance:
Leakage reactance refers to the reactance caused by the leakage flux in a transformer. It is an undesirable characteristic of a transformer and is usually kept low to improve efficiency. However, in the case of an auto transformer used with a sodium vapor lamp, a high leakage reactance is desirable. Here's why:

- Sodium vapor lamps operate at a high voltage, typically around 100-250 volts. To operate the lamp, the supply voltage needs to be step up to this level. An auto transformer is used for this purpose.

- When an auto transformer is used to step up the voltage, a high leakage reactance helps in limiting the current flow. This is important because sodium vapor lamps have a negative impedance characteristic, meaning that as the current through the lamp increases, its voltage drop decreases. To maintain a stable operating condition, it is necessary to limit the current flowing through the lamp.

- By having a high leakage reactance in the auto transformer, the current flow to the lamp is limited, thus preventing excessive current and maintaining stable operation.

- Additionally, a high leakage reactance also helps in reducing losses in the auto transformer, improving its efficiency.

In conclusion, an auto transformer used with a sodium vapor lamp should have a high leakage reactance in order to limit the current flow and maintain stable operation. This helps in ensuring efficient and reliable operation of the sodium vapor lamp.