Question

Typical power-line lengths are only a small fraction of the wavelength.

(a) True

(b) False

Short answer

Therefore, the correct option is (a): True

Step-by-step solution

Determine the equation of the wavelength for the lossless line.

The equation of wavelength for the wavelength is given below,

$\mathbf{\lambda }\mathbf{=}\frac{\mathbf{1}}{\mathbf{f}\sqrt{\mathbf{LC}}}$ …… (1)

Here, $\mathbf{f}$ is the system frequency,$\mathbf{L}$ is the inductance and$\mathbf{C}$ is the capacitance of the lines.

Determine the values of the wavelength.

The velocity of the propagation of the current wave and voltage along lossless line is $\frac{1}{\sqrt{LC}}=3\times {10}^8\frac{\text{m}}{\text{s}}$.

Calculate the wavelength.

Substitute$3\times {10}^8\frac{\text{m}}{\text{s}}$ for$\frac{1}{\sqrt{LC}}$ into equation (1).

$\begin{array}{l}\lambda =\frac{3\times {10}^8}{60}\\ \lambda =5000\text{\hspace{0.17em}km}\end{array}$

Hence, typical power line length are only for the small fraction of the 60 Hz wavelength.