In a delta-connected system, how does the line current relate to the phase current?

In a delta-connected system, how does the line current relate to the phase current?

• A. Line current equals phase current
• B. Line current equals sqrt(3) times phase current
• C. Line current equals half the phase current
• D. Line current equals phase current divided by sqrt(3)

Answer: (B)

In a delta connection, each line carries the currents from two windings, so the line current is the vector difference of those two phase currents. In a balanced system those winding currents are 120 degrees apart, and when you combine two equal-magnitude phasors separated by 120 degrees, the resulting magnitude is sqrt(3) times the individual phase current. So the line current is sqrt(3) times the phase current. For example, if the phase current is 10 A, the line current is about 17.32 A. The other options don’t fit because they don’t reflect this phasor addition of two winding currents inherent to a delta connection.

In a delta connection, each line carries the currents from two windings, so the line current is the vector difference of those two phase currents. In a balanced system those winding currents are 120 degrees apart, and when you combine two equal-magnitude phasors separated by 120 degrees, the resulting magnitude is sqrt(3) times the individual phase current. So the line current is sqrt(3) times the phase current. For example, if the phase current is 10 A, the line current is about 17.32 A. The other options don’t fit because they don’t reflect this phasor addition of two winding currents inherent to a delta connection.