Determine the resistance of an ammeter.

[Asmaa Mohammad]

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

[/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?

 

[ehild]

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 (U_A) is not in phase with the voltage across the inductor (U_L)

 

[Asmaa Mohammad]

The voltage across the ammeter (U_A) is not in phase with the voltage across the inductor (U_L)
View attachment 196351

So, what should I do?

 

[ehild]

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.

 

[Asmaa Mohammad]

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?

 

[ehild]

You mean it will be like this?
View attachment 196357

Exactly! You did it!

 

[Asmaa Mohammad]

Exactly! You did it!

I checked my book and found it was the right answer. Thank you, ehild!