This question was previously asked in

ESE Electronics 2016 Paper 1: Official Paper

Option 2 : \(\sqrt{\frac{L}{C}}\) Ω

__Concept__:

The surge impedance or the characteristic impedance of a transmission line is given by:

\({Z_0} = \sqrt {\frac{{R\; + \;j\omega L}}{{G\; + \;j{\rm{\omega }}C}}}\) ---(1)

R = Resistance per unit length

L = Inductance per unit length

G = Conductance of dielectric per unit length

C = Capacitance per unit length.

The characteristic impedance of a transmission line is determined by the physical conditions or geometric configuration and materials of the line. For a uniform line, it is not dependent on length.

**Lossless: **For a lossless transmission line, the value of Resistance and conductance will be zero, i.e.

R = G = 0 for lossless transmission line.

Putting this in Equation (1), we get:

\(Z_0=\sqrt{\frac{L}{C}}~\Omega\)