Transformer Efficiency Calculations

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Discussion Overview

The discussion revolves around calculating the efficiency of a transformer, specifically a 500W transformer that reduces 230V AC to 24V. Participants explore the implications of copper losses and core losses in the efficiency calculations, addressing both theoretical and practical aspects of transformer operation.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant seeks guidance on calculating transformer efficiency using given resistances and core losses.
  • Another participant provides a formula for copper losses and performs calculations for both primary and secondary windings, arriving at a total efficiency of 99.07%.
  • A different participant questions the validity of the calculated secondary current based on the efficiency result, suggesting that the output power should not equal the input power if efficiency is less than 100%.
  • One participant clarifies that the 500W refers to output power, leading to a recalculation of input power and efficiency.
  • Another participant expresses confusion regarding the relationship between input power, current, and losses, questioning how the input power affects the primary winding losses.
  • A later reply suggests that while more power is lost, the input power also increases, implying that the percentage of loss remains constant.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of input and output power in transformer efficiency calculations. There is no consensus on the correct approach to resolving the confusion surrounding the relationship between input power, current, and losses.

Contextual Notes

Participants highlight potential misunderstandings regarding the definitions of input and output power, as well as the implications of efficiency on current and losses in the transformer. The discussion remains unresolved regarding the correct interpretation of these concepts.

MathsDude69
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Hey. I am currently doing a bit of revision for an exam and I am struggling on the following question:

Calculate the efficiency of a 500W transformer, which reduces the 230 AC voltage to 24 V. For the calculations, assume the resistances of the primary and secondary windings as 0.05 Ohm and 0.01 Ohm, respectively. The losses in the transformer core Pc = 70mW.

I understand the whole voltage/current/power/impedance ratio stuff, but can't seem to find any information on calculating efficiencies using the resistances or the transformer core losses. Any Suggestions?
 
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Hey. I've found a bit more information regarding copper losses in transformers. It states:

Copper Loss = Ip2Rp + Is2Rs

I would think given the question that the asnwer would be:

P = VI ∴ I = P/V

For the primary:
500/230 = 2.27 Amps

For the secondary:
500/24 = 20.83 Amps

Copper loss for primary:
2.272 x 0.05 = 0.258 W

Copper loss for secondary:
20.832 x 0.01 = 4.34 W

Total Copper Loss:
0.258 + 4.34 = 4.598 W

Total loss including core loss:

4.598 + 0.07 = 4.668 W

Total efficiency =
(500-4.668)/500 = 0.9907 = 99.07% efficient.

The problem with this is if we were only getting an efficiency of 99.07% the secondary wouldn't be developing 20.83 Amps! Does anyone know how to actually solve this question?
 
@ Maths:
I skimmed through this pretty fast but I would say that you should not have 500 watts for both the primary and secondary. With any efficiency of less than 100% you will naturally get you a lower secondary current than 20.83.
 
You are nearly there except for the last bit.

The 500W refers to the output not the input for transformers so

input power = output power + total losses = 500 + 4.668 = 504.668.

efficiency = 1 - losses/input power = 1 - 4.668/504.668 = 99.07% expressed as a percentage.
 
See this is where I am getting confused. If the input power is 504.668W instead of 500W wouldn't that make the current and thus the losses higher on the primary winding??
 
More power is lost, but more is put in too. The percentage of loss should be the same.
 

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