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A voltmeter has a resistance of G ohm and range V volt. The value of resistance used in series to convert it into voltmeter of range nV volt is
- a)nG
- b)(n−1)G
- c)G/n
- d)G/(n−1)
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A voltmeter has a resistance of G ohm and range V volt. The value of r...
We know that R=V/Ig−G
The voltmeter gives the full-scale deflection for potential difference V. Its resistance is G. Hence, In=(V/G).
Given that V=nV
The voltmeter gives the full-scale deflection for potential difference V. Its resistance is G. Hence, In=(V/G).
Given that V=nV
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A voltmeter has a resistance of G ohm and range V volt. The value of r...
Understanding Voltmeter Conversion
To convert a voltmeter of range V volts into a voltmeter of range nV volts, we need to consider the resistance of the voltmeter and the additional resistance required in series.
Principle of Operation
- A voltmeter measures the potential difference across its terminals.
- When converting to a higher range, we add a series resistance to ensure that the voltmeter can handle the increased voltage without damaging its internal components.
Given Parameters
- Resistance of the voltmeter = G ohm
- Original range of the voltmeter = V volts
- New desired range = nV volts
Calculating Series Resistance
1. Voltage Division: When a voltmeter with resistance G is connected in series with another resistance R, the voltage drop across the voltmeter is a fraction of the total voltage.
2. Using Voltage Ratios: The voltage across the voltmeter can be given by the ratio:
- V / (V + R) = G / (G + R)
3. Setting Up the Equation: For the new range of nV:
- nV / (nV + R) = G / (G + R)
4. Solving for R: Rearranging gives us:
- R = (n-1)G
This means the resistance required in series to achieve the desired range of nV volts is (n - 1)G ohms.
Conclusion
Thus, the correct answer for the resistance used in series to convert the voltmeter into one of range nV volts is option B: (n - 1)G. This ensures proper functioning and safety of the voltmeter under higher voltage conditions.
To convert a voltmeter of range V volts into a voltmeter of range nV volts, we need to consider the resistance of the voltmeter and the additional resistance required in series.
Principle of Operation
- A voltmeter measures the potential difference across its terminals.
- When converting to a higher range, we add a series resistance to ensure that the voltmeter can handle the increased voltage without damaging its internal components.
Given Parameters
- Resistance of the voltmeter = G ohm
- Original range of the voltmeter = V volts
- New desired range = nV volts
Calculating Series Resistance
1. Voltage Division: When a voltmeter with resistance G is connected in series with another resistance R, the voltage drop across the voltmeter is a fraction of the total voltage.
2. Using Voltage Ratios: The voltage across the voltmeter can be given by the ratio:
- V / (V + R) = G / (G + R)
3. Setting Up the Equation: For the new range of nV:
- nV / (nV + R) = G / (G + R)
4. Solving for R: Rearranging gives us:
- R = (n-1)G
This means the resistance required in series to achieve the desired range of nV volts is (n - 1)G ohms.
Conclusion
Thus, the correct answer for the resistance used in series to convert the voltmeter into one of range nV volts is option B: (n - 1)G. This ensures proper functioning and safety of the voltmeter under higher voltage conditions.
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