A 4400 Volt 60 Hz transformer has a core loss of 840 watts, of which one third is eddy current loss. Now what will be the core loss when the transformer is connected to a 4600 volt... A 4400 Volt 60 Hz transformer has a core loss of 840 watts, of which one third is eddy current loss. Now what will be the core loss when the transformer is connected to a 4600 volt 60 Hz source?
Understand the Problem
The question asks for the core loss in a transformer when connected to a different voltage source, given the initial core loss and the distribution of losses. It requires us to calculate the new loss based on these parameters.
Answer
The core loss when connected to a 4600 V source is approximately $875 \, \text{W}$.
Answer for screen readers
The core loss when the transformer is connected to a 4600 V source is approximately $875 , \text{W}$.
Steps to Solve
- Identify Given Values
The transformer has the following characteristics:
- Original Voltage ($V_1$) = 4400 V
- New Voltage ($V_2$) = 4600 V
- Original Core Loss ($P_{core}$) = 840 W
- Calculate the Eddy Current Loss
From the total core loss, one third is attributed to eddy current loss.
Calculate the eddy current loss: $$ P_{eddy} = \frac{1}{3} P_{core} = \frac{1}{3} \times 840 , \text{W} = 280 , \text{W} $$
- Calculate the Iron Loss
The remaining core loss is due to hysteresis and can be calculated as: $$ P_{hysteresis} = P_{core} - P_{eddy} = 840 , \text{W} - 280 , \text{W} = 560 , \text{W} $$
- Determine the New Core Loss Using Voltage Ratio
The core loss is proportional to the square of the voltage. Thus, the new core loss ($P_{core, new}$) can be computed using the voltage ratio: $$ P_{core, new} = P_{hysteresis} + P_{eddy} \cdot \left( \frac{V_2^2}{V_1^2} \right) $$
Calculate the ratio: $$ \frac{V_2^2}{V_1^2} = \left( \frac{4600}{4400} \right)^2 $$
- Calculating the New Core Loss
Substituting the values: $$ \frac{4600}{4400} = \frac{4600 \times 4600}{4400 \times 4400} $$
Calculate this: $$ P_{core, new} = 560 + 280 \cdot \left( \frac{4600^2}{4400^2} \right) $$
- Final Calculation
Calculate $P_{core, new}$ using the obtained ratio: $$ P_{core, new} = 560 + 280 \cdot \left( \frac{21160000}{19360000} \right) $$ Evaluate this to find the new core loss.
The core loss when the transformer is connected to a 4600 V source is approximately $875 , \text{W}$.
More Information
The core loss of a transformer significantly changes with variations in voltage. The core loss mainly consists of hysteresis and eddy current losses which are affected by the operating voltage.
Tips
- Incorrectly calculating the voltage ratio: Make sure to square the ratio of the voltages.
- Not distinguishing between different types of losses: Ensure to separate hysteresis loss from eddy current loss correctly before using them in calculations.
AI-generated content may contain errors. Please verify critical information
