Question

What is the characteristic impedance of a lossless transmission line?

• A. $\sqrt{\dfrac{R}{G}}$
• B. $\sqrt{\dfrac{L}{C}}$
• C. $\dfrac{R}{L}$
• D. $\dfrac{G}{C}$

Hint:

Lossless line → $R=0, G=0$ → $Z_0 = \sqrt{\dfrac{L}{C}}$.

Answer 1

The Correct Option is B

Concept: A transmission line is characterized by primary constants: resistance ($R$), inductance ($L$), conductance ($G$), and capacitance ($C$). The characteristic impedance depends on these parameters.
Step 1: General formula.
\[ Z_0 = \sqrt{\frac{R + j\omega L}{G + j\omega C}} \]
Step 2: Lossless condition.
For a lossless line: \[ R = 0, \quad G = 0 \]
Step 3: Simplified formula.
\[ Z_0 = \sqrt{\frac{j\omega L}{j\omega C}} = \sqrt{\frac{L}{C}} \]
Step 4: Conclusion.
Thus, the characteristic impedance of a lossless transmission line is $\sqrt{\dfrac{L}{C}}$.