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Ideal Transformers and finding the steady state current?

  • #1

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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Answers and Replies

  • #2
NascentOxygen
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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?
 
  • #3
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!
 
  • #4
rude man
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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.
 
  • #5
NascentOxygen
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Science Advisor
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  1. So,with a little thought experiment, you can remind yourself that the transformer transforms impedances according to n2.
 

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