Question

The three phase source line to neutral voltages are given by ${\mathit{E}}_{\mathbf{h}}\mathbf{=}\mathbf{10}\mathbf{\angle }\mathbf{0}\mathbf{°}\mathbf{,}\mathbf{}{\mathit{E}}_{\mathbf{b}\mathbf{h}}\mathbf{=}\mathbf{10}\mathbf{\angle }\mathbf{240}\mathbf{°}\mathbf{,}\mathbf{}$, and ${\mathit{E}}_{\mathbf{a}\mathbf{h}}\mathbf{=}\mathbf{10}\mathbf{\angle }\mathbf{-}\mathbf{240}\mathbf{°}\mathbf{,}\mathbf{}$ volts.

Is the source balanced.

(a) Yes

(b) No

Short answer

Answer

Therefore, the source is balanced and the correct option for the statement is “Yes”.

Step-by-step solution

Define balanced source

The source is considered as balanced when the voltages at the three phases have same magnitude and equal phase shift between any of the two phases.

Determine if the statement is true or false.

For the given condition,

$$\begin{gathered} E_{\mathrm{ah}}=10\angle 0° \\ {E}_{\mathrm{bh}}=10\angle 240° \\ {E}_{\mathrm{bh}}=10\angle -240°, \end{gathered}$$

The voltage have equal magnitude of 10 and the two phase. Since, the voltages $E_{\mathrm{bh}}=10\angle 240°$and $E_{\mathrm{bh}}=10\angle -120°$ are equal, also localid="1652688743091" $10\angle 120°=10\angle -240°$. Since, $E_{bh}$leads $E_{ch}$ by 120 degrees and leads $E_{bh}$ by 120 degree so the sequence is positive.

Since, the phase sequence is positive and the magntiudes are equals. So the source is balanced.

Thus, the statement is true.