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A 6600 v 50 hz transformer operates at flux density of 1.5 T. Each linear dimension of the core is doubled while the primary and secondary turns are halved. If transformer now operates ar 13200V 50 hz what will be the core flux density?
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A 6600 v 50 hz transformer operates at flux density of 1.5 T. Each lin...
Problem Statement:
A 6600 V 50 Hz transformer operates at a flux density of 1.5 T. Each linear dimension of the core is doubled while the primary and secondary turns are halved. If the transformer now operates at 13200 V 50 Hz, what will be the core flux density?
Solution:
Given:
- Voltage (V1) = 6600 V
- Frequency (f1) = 50 Hz
- Flux density (B1) = 1.5 T
- Primary and Secondary turns (N1 = N2) are halved
- Linear dimensions of the core are doubled
- Voltage (V2) = 13200 V
- Frequency (f2) = 50 Hz
Step 1: Calculate the voltage ratio
The voltage ratio is given by:
```
V2 / V1 = N2 / N1
```
Substituting the given values, we get:
```
13200 / 6600 = N2 / (N1 / 2)
N2 = N1
```
Therefore, the number of turns in the primary and secondary remain the same.
Step 2: Calculate the flux density
The flux density is given by:
```
B2 / B1 = (V2 / V1) * (f1 / f2) * (N1 / N2) * (l2 / l1)
```
where l is the mean length of the magnetic path.
Since the linear dimensions of the core are doubled, the mean length of the magnetic path is also doubled. Therefore,
```
l2 / l1 = 2
```
Substituting the given values, we get:
```
B2 / 1.5 = (13200 / 6600) * (50 / 50) * (1 / 1) * (2 / 1)
B2 = 3.0 T
```
Step 3: Conclusion
Therefore, the core flux density of the transformer operating at 13200 V 50 Hz is 3.0 T.
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A 6600 v 50 hz transformer operates at flux density of 1.5 T. Each linear dimension of the core is doubled while the primary and secondary turns are halved. If transformer now operates ar 13200V 50 hz what will be the core flux density?
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