Question

Given below are two statements, one is labelled as Assertion (A) and other one labelled as Reason (R).

Assertion (A): The copper losses of a single-phase induction motor are high compared to three phase induction motor
Reason (R): In a three-phase induction motor, the load current is distributed among multiple windings

In light of the above statements, choose the correct answer from the options given below.

• A. Both (A) and (R) are true and (R) is the correct explanation of (A).
• B. Both (A) and (R) are true but (R) is NOT the correct explanation of (A).
• C. (A) is true but (R) is false.
• D. (A) is false but (R) is true.

Hint:

For the same power output, a 3-phase system is always more efficient and compact than a 1-phase system because power is transferred continuously and split among three phases.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Copper loss in an electrical machine is given by \(I^2 R\), representing power dissipated as heat in the conductor windings.

Step 3: Detailed Explanation:
1.

Assertion (A): For a given power rating, a single-phase induction motor must carry all current through one main winding, operating at a lower power factor and efficiency compared to a three-phase motor.
This results in a much higher current in the single-phase winding, leading to higher copper losses (\(I^2 R\)). Thus, the Assertion is true.
2.

Reason (R): A three-phase induction motor distributes the total power across three separate phase windings.
This distribution means the phase current in each winding is significantly lower than the current in an equivalent single-phase motor, reducing the overall heat loss. Thus, the Reason is true.
Since the distribution of the current among three phases is the direct cause of the lower currents (and hence lower copper losses) in three-phase motors compared to single-phase motors, the Reason is the correct explanation of the Assertion.

Step 4: Final Answer:
The correct option is 1, which corresponds to both statements being true with the Reason correctly explaining the Assertion.