# Calculating voltage which voltmeter is showing

• akaliuseheal
In summary, the problem involves determining the voltage between two points in a circuit using different voltmeters with varying internal resistances. By setting up equations using Ohm's Law and the concept of current division, the voltage can be solved for and found to be 16V.
akaliuseheal

## Homework Statement

Schematic of circuit is not given, only the text which I translated into English.

Using a voltmeter with internal resistance of 6k ohm, voltage between two points, 1 and 2 of a circuit of constant current, is measured to be 8v.
Then, using a voltmeter with internal resistance of 10k ohm, between the same points, voltage is measured to be 12v.
What voltage will the voltmeter with internal resistance of 15k ohm measure?

I=U/R

## The Attempt at a Solution

I tried to solve it by calculating currents getting 1.3mA and 1.2mA in first and second case, but wasn't sure what to do next.
These voltmeters should be represented as resistors and the answer is 16V.

You're told that the current in the circuit is constant, which I take to mean that the current leaving node 2 is the same as the current entering node 1:

So ##I## is an unknown constant and ##R## is some unknown resistance lying between nodes 1 and 2. That's two unknowns. Fortunately you were given two cases where the meter resistance and the measured voltage are given, so you can construct two equations in two unknowns.

akaliuseheal
I would like to thank you for looking into this but I am unsure on how to do that. I mean, how would system of equations look like?

Start symbolically: don't plug in any numbers, just use variables. See if you can write an expression for the voltage ##V## in terms of ##I##, ##R## and ##R_m##. Or, write an expression for ##I## in terms of ##V##, ##R## and ##R_m##. Either way is fine (although the latter may be more straight forward).

So like voltage/current divider?
V = (Rm || R) * I

akaliuseheal said:
So like voltage/current divider?
V = (Rm || R) * I
Sure, that would work. Or since the voltage is the same across both resistors it's easy to write the sum of the currents:

##I = \frac{V}{R} + \frac{V}{R_m}##

Whatever you are more comfortable with.

akaliuseheal
So it's like this.

R=30k ohm
I = 0,0016A

Replacing those values gets me the voltage of 16V.
Thanks, was struggling with this trivial problem.

Glad I could help.

## 1. What is voltage and why is it important in a circuit?

Voltage is the measure of the electric potential difference between two points in a circuit. It is important because it determines the amount of current that will flow through the circuit and affects the overall performance of the circuit.

## 2. How does a voltmeter measure voltage?

A voltmeter is connected in parallel to the circuit and measures the potential difference between the two points it is connected to. It reads the voltage in units of volts (V).

## 3. What is the difference between AC and DC voltage?

AC (alternating current) voltage changes direction periodically, while DC (direct current) voltage flows in only one direction. AC voltage is used in most household outlets, while DC voltage is commonly used in batteries.

## 4. Can a voltmeter show a negative voltage?

Yes, a voltmeter can show a negative voltage. This means that the potential difference between the two points being measured is negative, indicating a flow of current in the opposite direction.

## 5. How can I use a voltmeter to troubleshoot a circuit?

A voltmeter can be used to measure the voltage at different points in a circuit to identify any potential issues. If the voltage reading is significantly lower than expected, it may indicate a problem with a component or a break in the circuit. Similarly, a higher than expected voltage reading may suggest a short circuit or other issue.

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