In a three-phase balanced system, if the phase voltage is represented as V_A = 230 <0°, then the voltage for phase B will be _____.

Explanation:

Three-Phase Balanced System Voltage Analysis

Definition: In a three-phase balanced system, the voltages of the three phases are equal in magnitude and symmetrically displaced by 120° in phase. This configuration ensures uniform power delivery and efficient operation, which is why three-phase systems are commonly used in electrical power distribution and industrial applications.

Given: Phase voltage for phase A is represented as VA = 230 ∠0°. We need to determine the voltage for phase B.

Analysis:

In a balanced three-phase system, the phase voltages are separated by 120° in phase. This means:

• The voltage for phase A is given as VA = 230 ∠0°.
• The voltage for phase B will lag phase A by 120° (or equivalently lead by -120°).
• The voltage for phase C will lag phase B by 120° (or equivalently lead phase A by -240°, which is equivalent to +120° in the phasor cycle).

Using the phasor representation:

• VA = 230 ∠0°
• VB = 230 ∠-120°
• VC = 230 ∠120°

Therefore, the voltage for phase B is VB = 230 ∠-120°.

This corresponds to Option 3, which is the correct answer.

Important Note: The negative sign in the angle for VB indicates that phase B lags phase A by 120°. This phase relationship is essential for maintaining the symmetry of the three-phase system.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: VB = 230 ∠90°

This option incorrectly states the phase angle of VB. In a balanced three-phase system, the phase angles of the voltages are separated by 120°, not 90°. A phase angle of 90° would correspond to a scenario different from the given balanced three-phase system.

Option 2: VB = 230 ∠120°

This option suggests that phase B leads phase A by 120°. However, in a balanced three-phase system, phase B lags phase A by 120°, not leads. This makes Option 2 incorrect.

Option 4: VB = 230 ∠100°

This option provides an arbitrary phase angle of 100°, which does not align with the symmetrical 120° phase separation in a balanced three-phase system. Hence, this option is incorrect.

Conclusion:

Understanding the phase relationships in a three-phase balanced system is crucial for correctly identifying the voltages of different phases. In this case, the voltage for phase B is determined to be VB = 230 ∠-120°, which corresponds to Option 3. The symmetrical phase separation of 120° between the voltages ensures efficient power delivery in three-phase systems.