In a three-phase system, the line-to-line voltage is how many times the line-to-neutral voltage?

In a three-phase system, the line-to-line voltage is how many times the line-to-neutral voltage?

• A. 1.0
• B. 1.732
• C. 2.0
• D. 3.0

Answer: (B)

In a balanced three-phase system, the line-to-line voltage is the vector difference between two phase voltages that are 120 degrees apart. The line-to-neutral voltage is the voltage of a single phase with respect to neutral. When you subtract two phase voltages 120° apart, the magnitude works out to sqrt(3) times the phase voltage: V_LL = sqrt( V_Ph^2 + V_Ph^2 − 2 V_Ph^2 cos 120° ) = sqrt(3) · V_Ph. So the line-to-line voltage is sqrt(3) times the line-to-neutral voltage, which is about 1.732 times larger.

In a balanced three-phase system, the line-to-line voltage is the vector difference between two phase voltages that are 120 degrees apart. The line-to-neutral voltage is the voltage of a single phase with respect to neutral. When you subtract two phase voltages 120° apart, the magnitude works out to sqrt(3) times the phase voltage: V_LL = sqrt( V_Ph^2 + V_Ph^2 − 2 V_Ph^2 cos 120° ) = sqrt(3) · V_Ph. So the line-to-line voltage is sqrt(3) times the line-to-neutral voltage, which is about 1.732 times larger.