Ideal Transformers and finding the steady state current?

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Discussion Overview

The discussion revolves around calculating the steady state current in a circuit involving an ideal transformer with a specified load. Participants explore the implications of transformer theory, impedance calculations, and the effects of different load configurations on current readings.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Exploratory

Main Points Raised

  • One participant presents an initial calculation for the steady state current using a combination of impedances and transformer ratios, expressing uncertainty about the correctness of the result.
  • Another participant questions the appropriate formula for calculating the impedance of an inductance at a given frequency, suggesting a thought experiment involving resistive loads on both the secondary and primary sides of the transformer.
  • A participant corrects their earlier impedance calculation, proposing a new equivalent impedance and discussing the implications for current and load resistance on the primary side.
  • There is a confirmation from another participant regarding the calculated load impedance when considering a resistive load on the secondary side.
  • One participant emphasizes the principle that transformers transform impedances according to the square of the turns ratio.

Areas of Agreement / Disagreement

Participants express differing views on the calculations and assumptions regarding impedance and current, with no consensus reached on the correct steady state current value or the implications of the transformer model.

Contextual Notes

Participants note potential errors in impedance calculations and the dependence on specific definitions and assumptions about the circuit elements, but these remain unresolved.

mikehsiao789
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Homework Statement



In the circuit shown the 120V, 60Hz source supplies the ideal load shown through an ideal 2:1 transformer. What steady state current would you expect to read on the rms ammeter shown (please find the picture attached)?

Homework Equations


Zeq = (1/Z1+ 1/Z2)^-1
Z1 = 10+j(60*10^-3)
Z2= 10
V/Z=I

The Attempt at a Solution


What I did first was at the right side I combined the impedances and got Zeq as 9.53+j1.5068. Then I transformed it over to the primary side by multiplying but it's ratio, which is two. I get 19.027 + j3.013. Then I use the relationship V/Z=I to obtain 120/(19.027+j3.013) = 6.15-j0.97 or 6.229A with a phase angle of -9 degrees. However I am not sure if I got the right answer (there are no solutions to this...) Help!
 

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▸ What formula should you use when calculating the impedance of a 10mH inductance at 60Hz??

Here's a thought experiment...

▸ Suppose you have a 60 watt resistive load on the secondary side (60V & 1A, so that implies the load is 60Ω). A 60 watt equivalent load if located on the primary side where the voltage is 120V would require a current of how much? This implies the equivalent load on the primary side must therefore be how many ohms?
 
I realized I made a mistake, the impedance should we Z1= 10 + j*60*2pi*10^-3 and Z2 remains the same... which would give me a Zeq of: 5.171+ j0.91.

Umm, if I had a 60 Watt resistive load on the secondary side, with 120V, the current on the primary side must be 0.5A, which means the load would be 240 Ohms?
Thanks so much for your help!
 
mikehsiao789 said:
I realized I made a mistake, the impedance should we Z1= 10 + j*60*2pi*10^-3 and Z2 remains the same...
Right.
Umm, if I had a 60 Watt resistive load on the secondary side, with 120V, the current on the primary side must be 0.5A, which means the load would be 240 Ohms?
Thanks so much for your help!
Yes, load looking from primary is 60*22 = 240 ohms.
 
  1. So,with a little thought experiment, you can remind yourself that the transformer transforms impedances according to n2.
 

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