In a three-phase system, what is the relationship between line-to-line voltage and phase voltage when connected in a Y configuration?

In a three-phase system, what is the relationship between line-to-line voltage and phase voltage when connected in a Y configuration?

• A. Phase voltage equals line-to-line voltage
• B. Phase voltage equals line-to-line voltage divided by sqrt(3)
• C. Phase voltage equals line-to-line voltage times sqrt(3)
• D. Phase voltage is independent of connection

Answer: (B)

In a balanced three-phase system wired in a Y configuration, each phase voltage is the line-to-neutral voltage, while the line-to-line voltage is the difference between two phase voltages that are 120 degrees apart. The phasor difference between two 120-degree-apart phase voltages has a magnitude of sqrt(3) times a single phase voltage, so V_LL = sqrt(3) × V_Ph. Therefore, the phase voltage is V_Ph = V_LL / sqrt(3). This is why the phase voltage is smaller by the factor sqrt(3) in a Y connection.

In a balanced three-phase system wired in a Y configuration, each phase voltage is the line-to-neutral voltage, while the line-to-line voltage is the difference between two phase voltages that are 120 degrees apart. The phasor difference between two 120-degree-apart phase voltages has a magnitude of sqrt(3) times a single phase voltage, so V_LL = sqrt(3) × V_Ph. Therefore, the phase voltage is V_Ph = V_LL / sqrt(3). This is why the phase voltage is smaller by the factor sqrt(3) in a Y connection.