The characteristic impedance of a loss -less transmission line is: given by:

Options

A. `Z_(0)=sqrt(LC)`
B. `Z_(0)=sqrt(L/C)`
C. `Z_(0)=sqrt(C/L)`
D. `Z_(0)=LC`

Answer

To find the characteristic impedance of a lossless transmission line, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition**: The characteristic impedance \( Z_0 \) of a transmission line is defined as:
\[ Z_0 = \sqrt{\frac{R + j\omega L}{G + j\omega C}} \]
where:
- \( R \) = resistance per unit length
- \( L \) = inductance per unit length
- \( G \) = conductance per unit length
- \( C \) = capacitance per unit length
- \( j \) = imaginary unit
- \( \omega \) = angular frequency

2. **Identify Lossless Conditions**: For a lossless transmission line, the resistance \( R \) and conductance \( G \) are both zero:
\[ R = 0 \quad \text{and} \quad G = 0 \]

3. **Substitute Values**: Substitute \( R \) and \( G \) into the characteristic impedance formula:
\[ Z_0 = \sqrt{\frac{0 + j\omega L}{0 + j\omega C}} = \sqrt{\frac{j\omega L}{j\omega C}} \]

4. **Simplify the Expression**: The \( j\omega \) terms cancel out:
\[ Z_0 = \sqrt{\frac{L}{C}} \]

5. **Final Result**: Therefore, the characteristic impedance for a lossless transmission line is:
\[ Z_0 = \sqrt{\frac{L}{C}} \]

### Conclusion:
The characteristic impedance of a lossless transmission line is given by:
\[ Z_0 = \sqrt{\frac{L}{C}} \]