Ideal Transformers and finding the steady state current?

AI Thread Summary
The discussion revolves around calculating the steady state current in a circuit with a 120V, 60Hz source and a 2:1 ideal transformer. The user initially calculated the equivalent impedance (Zeq) and derived a current of approximately 6.229A, but questioned the accuracy of their result. They later clarified their approach by considering a 60-watt resistive load on the secondary side, realizing that the equivalent load on the primary side would be 240 ohms, leading to a current of 0.5A. The conversation emphasizes the importance of correctly transforming impedances through the transformer ratio. Overall, the calculations and thought experiments highlight the relationship between voltage, current, and impedance in transformer circuits.
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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