$$C = \frac{2\pi\varepsilon l}{\ln(b/a)}$$
Where:
- C is the capacitance in Farads (F)
- ε is the permittivity of the material between the conductors (in F/m)
- l is the length of the cable (in m)
- a is the inner radius of the outer conductor (in m)
- b is the outer radius of the inner conductor (in m)
In this case, we have a coaxial cable with zero resistance, which means that the material between the conductors is a perfect conductor. Therefore, the permittivity of the material is infinite, and the capacitance becomes:
$$C = \frac{2\pi\varepsilon l}{\ln(b/a)} = \frac{2\pi\infty l}{\ln(b/a)} = \infty$$
This means that the capacitance of a coaxial cable with zero resistance is infinite, which is not physically possible.
