What is the characteristic impedance of a lossless transmission line having inductance of 100nH/m and capacitance of 40pF/m.

Concept:

The characteristic impedance \(Z_0\) of a lossless transmission line is given by:

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

Where,

• \(L\) = Inductance per unit length (in H/m)
• \(C\) = Capacitance per unit length (in F/m)

Given:

\(L = 100~\text{nH/m} = 100 \times 10^{-9}~\text{H/m}\)

\(C = 40~\text{pF/m} = 40 \times 10^{-12}~\text{F/m}\)

Calculation:

\(Z_0 = \sqrt{\frac{100 \times 10^{-9}}{40 \times 10^{-12}}} = \sqrt{\frac{100}{40} \times 10^3} = \sqrt{2.5 \times 10^3} = \sqrt{2500} = 50~\Omega\)

Hence, the correct answer is 3