In a star-connected system, the line voltage equals the phase voltage multiplied by √3.

In a star-connected system, the line voltage equals the phase voltage multiplied by √3.

• A. True
• B. False
• C. It is only true for delta connections
• D. V_line = √3 × V_phase

Answer: (D)

In a star (wye) connection, the line-to-line voltage is √3 times the phase (line-to-neutral) voltage. This comes from treating the three phase voltages as phasors separated by 120 degrees. The line voltage between two lines is the vector difference of two phase voltages, V_AB = V_A − V_B. If V_A = Vph ∠0° and V_B = Vph ∠−120°, the magnitude of their difference is |V_AB| = √3 · Vph. So the line voltage equals √3 times the phase voltage. For example, if the phase voltage is 230 V, the line-to-line voltage is 230 × √3 ≈ 400 V. This relationship does not hold in a delta connection, where the line voltage equals the phase voltage.

In a star (wye) connection, the line-to-line voltage is √3 times the phase (line-to-neutral) voltage. This comes from treating the three phase voltages as phasors separated by 120 degrees. The line voltage between two lines is the vector difference of two phase voltages, V_AB = V_A − V_B. If V_A = Vph ∠0° and V_B = Vph ∠−120°, the magnitude of their difference is |V_AB| = √3 · Vph. So the line voltage equals √3 times the phase voltage.

For example, if the phase voltage is 230 V, the line-to-line voltage is 230 × √3 ≈ 400 V. This relationship does not hold in a delta connection, where the line voltage equals the phase voltage.