Determine the resistance of an ammeter.

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SUMMARY

The discussion focuses on determining the resistance of a hot-wire ammeter connected in series with an AC source, where the rms output voltage is 260V and the ammeter reads 2A. The voltage ratio across the ammeter to the inductor is given as 5/12. The solution involves using the formula i=V/R and understanding the phase relationship between the voltages across the ammeter and the inductor, which are not in phase due to the inductive nature of the circuit. The correct approach involves vector addition of voltages as illustrated in a phasor diagram.

PREREQUISITES
  • Understanding of AC circuit theory
  • Familiarity with phasor diagrams
  • Knowledge of inductors and their behavior in circuits
  • Proficiency in using Ohm's Law (i=V/R)
NEXT STEPS
  • Study phasor analysis in AC circuits
  • Learn about the behavior of inductors in series circuits
  • Explore the concept of voltage phase relationships in AC systems
  • Review vector addition of electrical quantities
USEFUL FOR

Students studying electrical engineering, particularly those focusing on AC circuit analysis, as well as educators and professionals seeking to reinforce their understanding of ammeter resistance in inductive circuits.

Asmaa Mohammad
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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).

Homework Equations


1nxNk.jpg
[/B]
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 textbook, could you explain why?
 
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Asmaa Mohammad said:

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).

Homework Equations


View attachment 196344 [/B]
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 textbook, 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
 
ehild said:
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?
 
Asmaa Mohammad said:
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.
 
ehild said:
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
 
ehild said:
Exactly! You did it! :smile:
I checked my book and found it was the right answer. Thank you, ehild!
 

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