Two feeder branches deliver phasor currents A and A into a common node, both referred to the same voltage reference. The magnitude of the total current leaving the node is most nearly:
- (A)11.6 A
- (B)15.0 A
- (C)17.8 A
- (D)21.0 A
Show worked solution
Answer: (C)
Added in rectangular form, the two branch currents give a resultant of 17.8 A. The 65 degree phase separation is what holds the total below the 21 A arithmetic sum.
Phasor addition requires rectangular components, since the two branch currents differ in phase by 65 degrees.
Component-wise addition leaves a resultant almost aligned with the real axis, the imaginary parts nearly cancelling.
Magnitude of the resultant follows from its rectangular components.
FE Reference Handbook — Mathematics: Complex Numbers, Polar and Rectangular Forms
Why the other choices appear
- (A)Subtracts the phasors instead of adding them, giving sqrt(225 - 91.29) = 11.56 A.
- (B)Treats the two currents as orthogonal, giving sqrt(12^2 + 9^2) = 15.0 A.
- (D)Adds the magnitudes arithmetically, 12 + 9 = 21 A, ignoring the 65 degree phase separation.