Question

A coaxial cable used in a transmission line has an inner radius of $$0.10 mm$$ and an outer radius of $$0.60 mm$$ . Calculate the capacitance per meter for the cable. Assume that the space between the conductors is filled with polystyrene.

Answer 1

The capacitance of a cylindrical capacitor is given by :
$$C=kC_0=\dfrac{2\pi kε_0L}{ln(b/a)}$$
where $$C_0$$ is the capacitance without the dielectric, $$k$$ is the dielectric constant, $$L$$ is the length, $$a$$ is the inner radius, and $$b$$ is the outer radius. The capacitance per unit length of the cable is :
$$\dfrac{C}{L}=\dfrac{2\pi kε_0}{ln(b/a)}=\dfrac{2\pi(2.6)(8.85\times10^{-12}F/m)}{ln[(0.60mm)/(0.10mm)]}=8.1\times10^{-11}F/m=81pF/m.$$