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A galvanometer with a full scale current of 10 mA has a resistance of 500Ω. The multiplying power of 50Ω shunt with this galvanometer is
  • a)
    11
  • b)
    110
  • c)
    1110
  • d)
    1100
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A galvanometer with a full scale current of 10 mA has a resistance of ...
Rsh= R/(m−1) ⇒ 50 = 500/(m−1) ⇒ m = 11
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A galvanometer with a full scale current of 10 mA has a resistance of ...
Understanding the Galvanometer Setup
A galvanometer is a sensitive device used to detect and measure small electric currents. In this case, we are analyzing a galvanometer with the following specifications:
- Full scale current: 10 mA
- Resistance of the galvanometer (Rg): 500 Ω
To extend the range of this galvanometer, a shunt resistor (Rs) is used. Here, we have a shunt of 50 Ω.
Calculating the Shunt Resistor's Effect
The shunt resistor allows a portion of the current to bypass the galvanometer, thus preventing it from exceeding its full-scale reading. The total current (I) that flows through the circuit is divided between the galvanometer (Ig) and the shunt (Is):
- Total current (I) = Ig + Is
Using the known full-scale current of the galvanometer:
- Ig = 10 mA = 0.01 A
The current flowing through the shunt can be calculated using Ohm's law.
Determining the Multiplying Power
The multiplying power (M) is defined as the ratio of the total current to the full-scale current of the galvanometer:
M = I / Ig
To find the total current (I), we can use the voltage across both resistors. The voltage across the galvanometer is:
Vg = Ig * Rg = 0.01 A * 500 Ω = 5 V
The same voltage appears across the shunt resistor:
V = Is * Rs
From this, we can find Is:
5 V = Is * 50 Ω
Is = 5 V / 50 Ω = 0.1 A
Now, calculate the total current:
I = Ig + Is = 0.01 A + 0.1 A = 0.11 A
Now, we can find the multiplying power:
M = I / Ig = 0.11 A / 0.01 A = 11
Conclusion
Thus, the multiplying power of the 50 Ω shunt with this galvanometer is 11, confirming that the correct answer is option 'A'.
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A galvanometer with a full scale current of 10 mA has a resistance of 500Ω. The multiplying power of 50Ω shunt with this galvanometer isa)11b)110c)1110d)1100Correct answer is option 'A'. Can you explain this answer?
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