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Determine the resistance of an ammeter.

  • #1

Homework Statement


An inductor is connected in series with an AC source, the rms output voltage of it is 260V and a hot-wire ammeter reads 2A. If the ratio of the voltage across the ammeter to the voltage across the inductor is 5/12, determine the resistance of the ammeter. (Neglect the inductor resistance).
2. Homework Equations
1nxNk.jpg

i=V/R (where i is the current, V is the voltage and R is the resistance).

The Attempt at a Solution



(Va is the ammeter voltage and Vl is the inductor voltage)
My result is not what in my text book, could you explain why?
 

Answers and Replies

  • #2
ehild
Homework Helper
15,394
1,801

Homework Statement


An inductor is connected in series with an AC source, the rms output voltage of it is 260V and a hot-wire ammeter reads 2A. If the ratio of the voltage across the ammeter to the voltage across the inductor is 5/12, determine the resistance of the ammeter. (Neglect the inductor resistance).
2. Homework Equations
View attachment 196344

i=V/R (where i is the current, V is the voltage and R is the resistance).

The Attempt at a Solution



(Va is the ammeter voltage and Vl is the inductor voltage)
My result is not what in my text book, could you explain why?
The voltage across the ammeter (UA) is not in phase with the voltage across the inductor (UL)
upload_2017-4-23_13-4-14.png
 
  • #3
The voltage across the ammeter (UA) is not in phase with the voltage across the inductor (UL)
View attachment 196351
So, what should I do?
 
  • #4
ehild
Homework Helper
15,394
1,801
So, what should I do?
Look at the picture, it is the phasor diagram of the voltages. The resistance of the ammeter is in series with the inductor. The voltage across the inductor is 90°ahead of the voltage of the resistor. You have to add the voltages as vectors, and the resultant voltage (the red vector) is equal to the voltage of the AC generator.
 
  • #5
Look at the picture, it is the phasor diagram of the voltages. The resistance of the ammeter is in series with the inductor. The voltage across the inductor is 90°ahead of the voltage of the resistor. You have to add the voltages as vectors, and the resultant voltage (the red vector) is equal to the voltage of the AC generator.
You mean it will be like this?
exY0o.jpg
 
  • #6
ehild
Homework Helper
15,394
1,801
  • #7
Exactly! You did it! :smile:
I checked my book and found it was the right answer. Thank you, ehild!
 

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