How to Find the Reading of Voltmeters in a Circuit with Identical Resistors?

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In summary, in the given circuit with identical and ideal voltmeters and resistors, with a given voltage V and resistance R, the readings for each voltmeter are V1=V2=0 and V3=V/3. This is found by applying Kirchhoff's Law and solving for the currents in each branch, which are V/3R for branches CD and DE and 2V/3R for the branch connecting all three voltmeters.
  • #1
utkarshakash
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Homework Statement


In the circuit shown below, all three voltmeters are ideal and identical. Each resistor has the same given resistance R. Voltage V is also given. Find the reading of each voltmeter.


The Attempt at a Solution



i = 2V/3R
Applying Kirchhoff's Law to BACDE
V1+V2=0

Loop CDHFG
V1+V3=2V/3

Loop DEH
V2+V3=2V/3

Solving these three, I get incorrect answers.
 

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  • #2
You've calculated I incorrectly. Since the voltage V appears across 3 R's in series, I = V/(3R).
 
  • #3
phyzguy said:
You've calculated I incorrectly. Since the voltage V appears across 3 R's in series, I = V/(3R).

Oops! I used incorrect notation for current. The current in the circuit as a whole is 2V/3R. The currrents in individual branches are V/3R.
 
  • #4
utkarshakash said:
Oops! I used incorrect notation for current. The current in the circuit as a whole is 2V/3R. The currrents in individual branches are V/3R.

Correct. Does this solve your original problem?
 
  • #5
phyzguy said:
Correct. Does this solve your original problem?

No. The correct answers are V1=V2=V/9 and V3=2V/9
 
  • #6
utkarshakash said:
No. The correct answers are V1=V2=V/9 and V3=2V/9

If you've posted the problem correctly, I don't think that can be the correct answer. VC = VE = V/3, so V1 and V2 should both read 0 and V3 should read V/3.
 

Related to How to Find the Reading of Voltmeters in a Circuit with Identical Resistors?

1. What is the purpose of finding the reading of a voltmeter?

The purpose of finding the reading of a voltmeter is to measure the electrical potential difference, or voltage, between two points in a circuit. This allows us to understand the flow of electricity and determine if the circuit is functioning properly.

2. How do I use a voltmeter to find the reading?

To find the reading of a voltmeter, first make sure it is set to the correct range for the expected voltage. Then, connect the voltmeter in parallel to the circuit, with the positive lead connected to the higher potential point and the negative lead connected to the lower potential point. Finally, read the value displayed on the voltmeter.

3. What are the units of measurement for a voltmeter reading?

The units of measurement for a voltmeter reading are volts (V) or millivolts (mV). Voltmeters can also be set to measure in other units such as kilovolts (kV) or microvolts (μV) depending on the range selected.

4. How accurate are voltmeter readings?

The accuracy of voltmeter readings depends on the quality and calibration of the voltmeter itself. Most voltmeters have an accuracy of around 1-2%, meaning that the actual value may vary slightly from the displayed reading. It is important to calibrate voltmeters regularly to ensure accurate readings.

5. Can I use a voltmeter to measure AC and DC voltage?

Yes, most modern voltmeters are able to measure both AC and DC voltage. It is important to make sure the voltmeter is set to the correct range for the type of voltage being measured, as AC voltage can fluctuate rapidly while DC voltage remains constant.

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