Reading of a voltmeter having resistance R across a resistance

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SUMMARY

The discussion centers on the calculation of the voltmeter reading (V') when measuring the potential difference across a resistor (R) in a circuit. The formula derived is V' = Ir/(R+r), where r is the resistance of the voltmeter. The participants emphasize the need for a circuit diagram to clarify the configuration of resistors and confirm that the total current remains constant (I' = I) for accurate readings. Additionally, there is a note on the dimensional correctness of the equation, indicating a potential typo in the solution.

PREREQUISITES
  • Understanding of Ohm's Law (V = IR)
  • Knowledge of series and parallel resistor configurations
  • Familiarity with circuit analysis techniques
  • Basic principles of electrical measurement
NEXT STEPS
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  • Learn about the impact of measuring instruments on circuit behavior
  • Explore the concept of equivalent resistance in mixed resistor configurations
  • Investigate the principles of accurate voltage measurement techniques
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Students in electrical engineering, physics enthusiasts, and anyone involved in circuit design and analysis will benefit from this discussion.

Shivang kohlii
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Homework Statement



The potential difference across resistance R carrying current I is V = IR . Now if the potential difference is measured via voltmeter of resistance r , the reading on voltmeter is V' . Prove that V' = Ir/(R+r) . For what value of r does the voltmeter measure true value

Homework Equations


V=ir

The Attempt at a Solution


Initially , V = IR
FINALLY, Rnet = R × r / ( R + r)
V' = I' Rnet , where I' is telhe new current in circuit..
I don't know how to proceed
 
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Shivang kohlii said:
Prove that V' = Ir/(R+r)
That would be hard to prove since as a general statement, it's not true. You need to draw a circuit diagram and show the resistors. Are they in series? Are they in parallel? Are they even in the same part of the circuit?
 
Shivang kohlii said:
V' = Ir/(R+r) .
This looks dimensionally incorrect. The RHS has dimensions of current.
 
Looks like a typo in the solution. Missing R?

I believe you are also meant to assume the total current flowing stays the same. So I'=I.
 

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