# Tension measured by a voltmeter of given bottom scale and current range

• greg_rack
In summary: Kirchhoff's 2nd law states that the current through a circuit is equal to the sum of the currents through each of the circuit's components.
greg_rack
Gold Member
Homework Statement
For measuring tension, a voltmeter uses a part of the current flowing through the circuit.
Subsequently, the tension measured is just an approximation of the one present when the voltmeter is not connected.
Consider a circuit formed by two ##1550\Omega## resistors connected in series powered by a ##60.0V## battery:
\rightarrow Find the tension of the two resistors.

An analogic voltmeter has a bottom scale of ##60.0V## and uses a galvanometer with a maximum current range of ##5.00mA##:
\rightarrow Find the tension measured by this voltmeter when it's connected to the ends of the resistors.
Relevant Equations
##I=\frac{V}{R}##
First and foremost, I've studied voltmeters and ammeters on my own, and online there aren't many resources to do so... forgive me in advance for eventual silly questions/doubts :)

I managed to calculate(intuitively) a tension of ##30.0V## per resistor, with basic procedures.

However, I'm finding difficulties in solving the second point.
What does the "bottom scale" mean? Isn't it simply the maximum tension that can be measured by this tool? Also, how should I use the "maximum current range" data?
Lastly: If the voltmeter must be precise, how could this result be different from that calculated in the first point?

greg_rack said:
What does the "bottom scale" mean?
Many voltmeters and ammeters have a second scale, usually the upper one, used for some other purpose. Don't worry about it.
greg_rack said:
how should I use the "maximum current range" data?
I believe that would be the current through the galvanometer at max deflection.

haruspex said:
I believe that would be the current through the galvanometer at max deflection.
And how could I apply it to my specific case? How do I know the current flowing through the galvanometer?

I still don't understand that if the voltmeter must be precise, how could the result of the 2nd point be different from that calculated in the first point? (it's 28.1V instead of 30V)

greg_rack said:
How do I know the current flowing through the galvanometer?
It tells you that if the voltmeter reads 60V then the current through it is 5mA.
So what is the resistance of the galvanometer?

Draw a circuit diagram showing the three resistances. With 60V applied, what will the galvanometer read?

greg_rack
haruspex said:
It tells you that if the voltmeter reads 60V then the current through it is 5mA.
Oh ok then, now it's clear! The internal resistance is going to be ##R_{G}=\frac{60V}{5\cdot 10^{-3}A}##

haruspex said:
Draw a circuit diagram showing the three resistances. With 60V applied, what will the galvanometer read?
so, this is my circuit
Considering the internal resistance of the galvanometer, it will "absorb" a current of ##I_{G}=\frac{60.0V}{R_{G}}##, which will be subtracted to that one flowing through the resistor... so it will measure a voltage ##V=(I_{initial}-I_{G})\cdot 1550\Omega##.
Does it make any sense?

greg_rack said:
View attachment 271902so, this is my circuit
Considering the internal resistance of the galvanometer, it will "absorb" a current of ##I_{G}=\frac{60.0V}{R_{G}}##,
Is the voltage across it 60V?
What current will flow around the circuit?

haruspex said:
Is the voltage across it 60V?
Right, the voltage across it is 30V.

haruspex said:
What current will flow around the circuit?
Do you mean the current with or without the galvanometer applied? Which of the two is relevant?

greg_rack said:
Do you mean the current with or without the galvanometer applied? Which of the two is relevant?
Auto-quote: I've managed to solve the problem applying Kirchhoff's 2nd law, @haruspex:

DaveE

## 1. What is the purpose of measuring tension with a voltmeter?

The purpose of measuring tension with a voltmeter is to determine the potential difference between two points in an electrical circuit. This can help determine the amount of electrical energy being used or transferred in a circuit.

## 2. How does a voltmeter measure tension?

A voltmeter measures tension by connecting two points in an electrical circuit and measuring the potential difference between them. This is typically done by using a sensitive galvanometer and a series of resistors to measure the voltage drop across the circuit.

## 3. What is the significance of the bottom scale on a voltmeter?

The bottom scale on a voltmeter indicates the range of voltage that the voltmeter is capable of measuring. This allows the user to select the appropriate range for the specific circuit being measured, ensuring accurate readings.

## 4. How does the current range affect the measurement of tension with a voltmeter?

The current range on a voltmeter determines the amount of current that can flow through the device without causing damage. If the current exceeds the range, the voltmeter may become damaged or provide inaccurate readings. It is important to select the appropriate current range for the circuit being measured.

## 5. Can a voltmeter measure tension in both AC and DC circuits?

Yes, a voltmeter can measure tension in both AC (alternating current) and DC (direct current) circuits. However, the type of voltmeter used may differ depending on the type of current being measured. AC voltmeters typically use a different scale and may have additional features to measure the frequency of the current.

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