Reading of a voltmeter having resistance R across a resistance

In summary, the conversation is about proving that the potential difference measured by a voltmeter with resistance r is V' = Ir/(R+r). The discussion also mentions the need to draw a circuit diagram and consider the placement of resistors, as well as the requirement for the total current to remain constant. There is also a potential typo in the solution, with a missing R on the right-hand side.
  • #1
Shivang kohlii
19
1

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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  • #2
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?
 
  • #3
Shivang kohlii said:
V' = Ir/(R+r) .
This looks dimensionally incorrect. The RHS has dimensions of current.
 
  • #4
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.
 

1. What is a voltmeter and how does it work?

A voltmeter is a device used to measure the potential difference, or voltage, between two points in an electric circuit. It typically consists of a display and two probes, one positive and one negative. The probe tips are placed across the two points being measured and the display shows the voltage in either volts or millivolts.

2. What is resistance and how does it affect the reading on a voltmeter?

Resistance is the measure of opposition to the flow of electric current through a material. When a voltmeter is used to measure voltage across a resistor, the resistor's resistance can affect the reading. This is because the voltage drop across the resistor will be proportional to the resistance, according to Ohm's law (V=IR).

3. Can a voltmeter measure the resistance of a component?

No, a voltmeter is not designed to measure resistance. To measure resistance, a multimeter or ohmmeter should be used. A voltmeter will only show the voltage drop across the component, which can then be used to calculate the resistance using Ohm's law.

4. How does the resistance of the voltmeter itself affect the measurement?

The resistance of the voltmeter can affect the measurement in two ways. First, the voltmeter should have a high resistance compared to the circuit being measured, otherwise it will draw current and affect the circuit's behavior. Second, the resistance of the voltmeter can cause a small error in the measurement. To minimize this error, the voltmeter should have a high input impedance, meaning it has a high resistance and draws very little current from the circuit being measured.

5. What are some common mistakes to avoid when using a voltmeter to measure resistance?

One common mistake is forgetting to set the voltmeter to the appropriate range. If the voltage being measured is too high for the selected range, it can damage the voltmeter or give inaccurate readings. Additionally, the probes should be placed in parallel with the component being measured. Placing them in series will result in incorrect readings. It's also important to make sure the circuit is not powered while taking resistance measurements, as this can damage the voltmeter or cause incorrect readings.

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