Select the option that is correct regarding the following two statements labelled Assertion (A) and Reason (R).

Assertion (A): The neutral wire in a star-connected balanced three-phase system carries no current.

Reason (R): In a balanced system, the sum of the three-phase current phasors is always zero. 

Explanation:

Assertion (A): The neutral wire in a star-connected balanced three-phase system carries no current.

Reason (R): In a balanced system, the sum of the three-phase current phasors is always zero.

Correct Option Analysis:

The correct option is:

Option 4: Both A and R are true, and R is the correct explanation of A.

Explanation:

In a star-connected balanced three-phase system, the load on all three phases is equal in magnitude and phase angle. This means the currents in the three phases are equal in magnitude but are separated by a phase difference of 120°. The phasor sum of the three-phase currents in such a system is always zero. Mathematically, if the three currents are represented as:

• I_a = I∠0°
• I_b = I∠-120°
• I_c = I∠120°

Then, the phasor sum of the currents is:

I_a + I_b + I_c = I∠0° + I∠-120° + I∠120° = 0

This means that the current flowing through the neutral wire, which is meant to carry the unbalanced current in the system, is zero in a balanced system. Therefore, the neutral wire does not carry any current in such cases.

The reason (R) directly explains the assertion (A). Since the phasor sum of the three-phase currents is zero in a balanced system, there is no resultant current to flow through the neutral wire. Hence, both the assertion and the reason are true, and the reason is the correct explanation of the assertion.

Additional Information:

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

Option 1: A is true, but R is false.

This option is incorrect because the reason (R) is also true. The phasor sum of the three-phase currents in a balanced system is indeed zero, and this is the fundamental explanation for the neutral wire carrying no current in such systems.

Option 2: A is false, but R is true.

This option is incorrect because the assertion (A) is true. In a balanced system, the neutral wire does not carry any current, as explained earlier.

Option 3: Both A and R are true, but R is not the correct explanation of A.

This option is incorrect because the reason (R) is directly related to and explains the assertion (A). The fact that the phasor sum of the three-phase currents is zero is the reason why the neutral wire carries no current in a balanced system.

Conclusion:

In a star-connected balanced three-phase system, the neutral wire carries no current because the phasor sum of the three-phase currents is always zero. This is a fundamental property of balanced three-phase systems and highlights the importance of symmetry in electrical systems. The correct option is Option 4, as both the assertion and the reason are true, and the reason correctly explains the assertion.