Question

In equivalent $\pi$ circuits of lossless lines, Z' is pure____ and Y' pure______.

Short answer

The $\pi$equivalent circuit of lossless line, Z' is purely inductive and Y' is purely capacitive

Step-by-step solution

Determine the equation to calculate the parameter of π.

The equation for the calculation of the Z' is given below,

$Z\text{'}=j\omega L\left(\frac{sin\beta l}{\beta l}\right)$ …… (1)

Here, $\beta$ is the phase constant.

The equation for the calculation of Y' is given below,

$\frac{Y\text{'}}{2}=\frac{j\omega C}{2}\left[\frac{tan\left(\frac{\beta l}{2}\right)}{\frac{\beta l}{2}}\right]$

Determine the nature of the Z' and Y' .

Since the inductance is present in the equation of the Z' parameter of the $\pi$equivalent circuit, therefore the Z' parameter purely inductive.

Similarly, the capacitance is present in the Y' parameter of the $\pi$equivalent circuit, therefore, Y' parameter is purely is purely capacitive.

Therefore, $\pi$equivalent circuit of lossless line, Z' is purely inductive and Y' is purely capacitive.