Understanding Voltage in Star Connected Circuits

In a three-phase electrical system, components can be connected in either a star (Y) or delta (Δ) configuration. The relationship between the voltage measured between any two lines (line voltage, \(V_L\)) and the voltage measured between a line and the neutral point (phase voltage, \(V_P\)) depends on the connection type.

For a star-connected circuit, there is a specific relationship between the line voltage and the phase voltage. The line voltage is \(\sqrt{3}\) times the phase voltage. This is because the line voltage is the vector sum of two phase voltages that are 120 degrees apart in phase.

The formula relating line voltage (\(V_L\)) and phase voltage (\(V_P\)) in a star connection is:

\( V_L = \sqrt{3} \times V_P \)

The question provides the value of the phase voltage in a star connected circuit:

• Phase Voltage (\(V_P\)) = 240 V

We need to find the line voltage (\(V_L\)). Using the formula for a star connection:

\( V_L = \sqrt{3} \times 240 \, \text{V} \)

We know that the approximate value of \(\sqrt{3}\) is 1.732.

\( V_L \approx 1.732 \times 240 \, \text{V} \)

Let's calculate the value:

\( V_L \approx 415.68 \, \text{V} \)

Now, let's compare this calculated value with the given options:

Our calculated value of approximately 415.68 V is very close to 415 V. Standard voltage values in many electrical systems are often rounded or nominal. For example, a 230V phase voltage often corresponds to a 400V line voltage (\(\sqrt{3} \times 230 \approx 398.4\)), and a 240V phase voltage often corresponds to a 415V line voltage (\(\sqrt{3} \times 240 \approx 415.7\)).

Therefore, based on the calculation and common standard voltage levels, the line voltage corresponding to a 240 V phase voltage in a star connected circuit is 415 V.

Revision Table: Star Connection Voltages

Additional Information: Star vs. Delta Connection

Understanding the difference between star and delta connections is crucial in three-phase systems:

• Star (Y) Connection:
  • Three phases are connected to a common neutral point.
  • Phase voltage is between phase and neutral.
  • Line voltage is between two lines.
  • Relationship: \( V_L = \sqrt{3} \times V_P \) and \( I_L = I_P \) (Line current equals phase current).
• Delta (Δ) Connection:
  • Phases are connected end-to-end, forming a closed loop.
  • No neutral point (unless derived externally).
  • Phase voltage is equal to line voltage.
  • Relationship: \( V_L = V_P \) and \( I_L = \sqrt{3} \times I_P \) (Line current is \(\sqrt{3}\) times phase current).

This question specifically deals with the star connected circuit, where the line voltage is always higher than the phase voltage by a factor of \(\sqrt{3}\).