Introduction:
The breakdown strength of an insulating oil refers to its ability to withstand electrical stress without experiencing electrical breakdown. It is an important property to consider when selecting an oil for electrical equipment such as transformers, capacitors, and cables.

Explanation:
Among the given options, silicon oil has the highest breakdown strength. Here's why:

Cable Oil:
- Cable oil is specifically formulated for use in power cables to provide insulation and cooling.
- It has good electrical properties but generally has lower breakdown strength compared to other insulating oils.

Transformer Oil:
- Transformer oil is used in electrical transformers to provide insulation and cooling.
- It is highly refined mineral oil with additives to enhance its electrical properties.
- Transformer oil has good breakdown strength, but it is not the highest among the given options.

Capacitor Oil:
- Capacitor oil is used in electrical capacitors to provide insulation and cooling.
- It is similar to transformer oil but may have different additives depending on the specific application.
- Capacitor oil has good breakdown strength, but it is not the highest among the given options.

Silicon Oil:
- Silicon oil, also known as silicone oil, is a synthetic oil composed of silicon atoms.
- It has excellent electrical properties and high breakdown strength, making it suitable for various electrical applications.
- Silicon oil can withstand higher electrical stress before experiencing breakdown compared to other insulating oils.
- It is commonly used in high-voltage equipment, such as high-voltage cables and power transformers.

Conclusion:
In summary, among the given options, silicon oil has the highest breakdown strength. It is preferred for applications where high electrical stress needs to be withstood without experiencing electrical breakdown.