Topic: Electromagnetics
The velocity at which a sinusoidal signal of $10^{9}~\text{rad/s}$ travels down a loss-less transmission line for which $L=0.4~\mu\text{H/m}$ and $C=40~\text{pF/m}$ is
- A. $2.36\times 10^{8}~\text{m/s}$
- B. $2.5\times 10^{8}~\text{m/s}$
- C. $5\times 10^{9}~\text{m/s}$
- D. $4.5\times 10^{9}~\text{m/s}$
Answer: B. $2.5\times 10^{8}~\text{m/s}$
Explanation: The phase velocity for a lossless transmission line is $v_{p} = \frac{1}{\sqrt{LC}}$.
$v_{p} = \frac{1}{\sqrt{0.4 \times 10^{-6} \times 40 \times 10^{-12}}}$
$= \frac{1}{\sqrt{16 \times 10^{-18}}} = \frac{1}{4 \times 10^{-9}}$
$= 0.25 \times 10^{9} = 2.5 \times 10^{8}~\text{m/sec}$.