If the speed of rotation of a separately excited dc machine is halved ...
Explanation:
To understand why the emf induced in the armature of a separately excited DC machine reduces to 1/4th of the original value when the speed of rotation is halved and the field strength is reduced to half, let's break down the process step by step.
1. Emf Induced in the Armature:
The emf induced in the armature of a DC machine is given by the equation:
E = kΦNZ/60A
Where:
- E is the induced emf
- k is a constant
- Φ is the flux per pole
- N is the speed of rotation in RPM
- Z is the total number of armature conductors
- A is the number of parallel paths
2. Effect of Halving the Speed of Rotation:
When the speed of rotation is halved, the value of N in the equation is reduced to half. Therefore, the induced emf is also reduced to half of its original value.
3. Effect of Reducing the Field Strength to Half:
The field strength is determined by the flux per pole (Φ). When the field strength is reduced to half, the value of Φ is also reduced to half.
4. Combined Effect:
Now, let's consider the combined effect of halving the speed of rotation and reducing the field strength to half.
- The induced emf is reduced to half due to the halving of the speed of rotation.
- Additionally, the induced emf is reduced to half again due to the reduction in field strength.
Therefore, the combined effect is such that the induced emf reduces to 1/4th (half * half) of its original value.
Conclusion:
Hence, the correct answer is option 'A' - the emf induced in the armature reduces to 1/4th of the original when the speed of rotation is halved and the field strength is reduced to half.