An underground cable has an insulation of relative permittivity of 2. If the insulating material is replaced by another material of relative permittivity of 4. Then capacitance of cable is:

Correct option is B

​$$\textbf{Explanation:} \text{The capacitance } (C) \text{ of a cable is directly proportional to the relative permittivity } (\varepsilon_r) \text{ of the insulating material.} \text{The relationship can be expressed as:}$$​$$C \propto \varepsilon_r$$

$$\textbf{Given:}$$

$$\begin{array}{ll}\bullet \quad \text{Initial relative permittivity } (\varepsilon_{r1}) = 2 \\\bullet \quad \text{New relative permittivity } (\varepsilon_{r2}) = 4\end{array}$$

$$\text{The new capacitance } (C_2) \text{ relative to the initial capacitance } (C_1) \text{ is:}$$

$$\frac{C_2}{C_1} = \frac{\varepsilon_2}{\varepsilon_1}$$

$$\frac{C_2}{C_1} = \frac{4}{2} = 2$$​​​​​​​