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

Step 1: Understanding the Concept:
The characteristic impedance ($Z_0$) is the ratio of voltage and current waves in a transmission line.
Step 2: Key Formula or Approach:
The general formula is:
\[ Z_0 = \sqrt{\frac{R + j\omega L}{G + j\omega C}} \]
Step 3: Detailed Explanation:
For a lossless line, the resistance ($R$) and conductance ($G$) are zero.
Substituting $R = 0$ and $G = 0$:
\[ Z_0 = \sqrt{\frac{j\omega L}{j\omega C}} = \sqrt{\frac{L}{C}} \]
Step 4: Final Answer:
The characteristic impedance is $\sqrt{L/C}$.