Join 60,000+ competitive exam aspirants
or with email
Your Cart
Subtotal₹0
Total₹0
Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
Join 60,000+ competitive exam aspirants
Vector sum of three phase voltage is
0
1
∞
120
0
In a balanced three-phase system, the three voltage vectors are equal in magnitude and displaced by 120° from each other. Consequently, their phasor sum is exactly zero at any instant.
In a balanced three-phase system, the three voltage vectors are equal in magnitude and displaced by 120° from each other. Consequently, their phasor sum is exactly zero at any instant.
Vtotal=VR+VY+VB=0
Vm(sin(ωt)+sin(ωt−120°)+sin(ωt−240°))=0
The three-phase voltages are represented as VR=Vm∠0°, VY=Vm∠−120°, and VB=Vm∠−240°. By applying Kirchhoff's Voltage Law or vector addition: VR+VY+VB=Vm(cos0+jsin0+cos120+jsin120+cos240+jsin240), which simplifies to zero.
This property holds strictly for balanced three-phase systems.
The phase displacement of 120° ensures the net displacement is zero.
In star-connected systems, this principle implies the neutral current IN is zero for balanced loads.
Constant power delivery
Reduction in neutral conductor current for balanced loads
Unbalanced loads lead to non-zero neutral current
Requires three-phase balanced supply for optimal efficiency
Three-phase industrial power distribution
AC induction motor stators
If the load is unbalanced, the vector sum of currents IR+IY+IB is not zero, and current flows through the neutral wire.
Option B, C, and D are incorrect as they represent non-zero scalar values or phase angles rather than the result of the vector addition.
A is correct — The vector sum of a balanced three-phase voltage system is equal to 0.
Always remember that while the vector sum is zero, the RMS phase-to-phase voltage is 3 times the phase voltage (VL=3Vph).