Galvanometer to Ammeter Conversion: Shunt Resistance Calculation
This problem involves converting a galvanometer into an ammeter using a shunt resistor. We need to calculate the value of this shunt resistor.
Given Information
- Galvanometer resistance, $G = 100 \ \Omega$
- Galvanometer full-scale deflection current, $I_g = 1 \text{ mA} = 1 \times 10^{-3} \text{ A}$
- Desired ammeter range (maximum current), $I = 10 \text{ A}$
Shunt Resistance Formula
To convert a galvanometer into an ammeter, a low resistance shunt ($S$) is connected in parallel with the galvanometer. The formula to calculate the shunt resistance is:
$S = \frac{G \times I_g}{I - I_g}$
Calculation Steps
-
Substitute the given values into the formula:
$S = \frac{100 \ \Omega \times (1 \times 10^{-3} \text{ A})}{10 \text{ A} - (1 \times 10^{-3} \text{ A})}$
-
Simplify the numerator:
$100 \ \Omega \times 0.001 \text{ A} = 0.1 \text{ V}$
-
Simplify the denominator:
$10 \text{ A} - 0.001 \text{ A} = 9.999 \text{ A}$
-
Calculate the shunt resistance $S$:
$S = \frac{0.1 \text{ V}}{9.999 \text{ A}} \approx 0.010001 \ \Omega$
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Rounding to a practical value, the required shunt resistance is approximately $0.01 \ \Omega$.
Conclusion
The calculated shunt resistance required to convert the galvanometer into an ammeter with a range of 0-10 A is $0.01 \ \Omega$.
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