Question

For the balanced three phase system ${\mathit{Z}}_{\mathbf{b}\mathbf{a}\mathbf{s}\mathbf{e}}$ is given by

${\mathit{Z}}_{\mathbf{b}\mathbf{a}\mathbf{s}\mathbf{e}}\mathbf{}\mathbf{=}\mathbf{}\frac{{\mathbf{V}}_{\mathbf{b}\mathbf{a}\mathbf{s}\mathbf{e}\mathbf{}\mathbf{L}\mathbf{L}}^{\mathbf{2}}}{{\mathbf{S}}_{\mathbf{b}\mathbf{a}\mathbf{s}\mathbf{e}\mathbf{3}}}$

Short answer

Therefore, the correct option is (a): True.

Step-by-step solution

Calculate the base current for the system.

Base voltage,$V_{base}=\frac{V_{baseLL}}{\sqrt{3}}$

Base current is given as

$I_{base}=\frac{S_{base3}}{\sqrt{3}{V}_{baseLL}}$

Here,$S_{base3}$ is the base power rating

determine the base impedance.

The base impedance can be calculated as

$Z_{base}=\frac{V_{baseLN}}{I_{base}}$

Substitute the expressions and solve as

$$\begin{gathered} Z_{base}=\frac{{\displaystyle \frac{V_{baseLL}}{\sqrt{3}}}}{{\displaystyle \frac{S_{base3}}{\sqrt{3}{V}_{baseLL}}}} \\ {Z}_{base}=\frac{V_{baseLL}^2}{S_{base3}} \end{gathered}$$

Hence the base impedance is given by

$Z_{base}=\frac{V_{baseLL}^2}{S_{base3}}$