An ammeter of 1 mA possesses a resistance of 100 ohms. This ammeter is to be converted into 1A ammeter. The value of shunt resistance required will be :
0.1001 Ω
To convert an ammeter with a full-scale deflection current of 1 mA and an internal resistance of 100 Ω into an ammeter that can measure up to 1 A, we need to determine the appropriate shunt resistance. The shunt resistor is connected in parallel with the ammeter to allow most of the current to bypass the meter, thereby preventing it from being damaged by excessive current.
Let's denote:
- \(I_g\): Full-scale deflection current of the ammeter = 1 mA = 0.001 A
- \(R_g\): Internal resistance of the ammeter = 100 Ω
- \(I\): Desired full-scale current of the modified ammeter = 1 A
- \(R_s\): Required shunt resistance
The current division in the ammeter setup is such that the internal ammeter current \(I_g\) plus the current through the shunt \(I_s\) equals the total current \(I\):
\(I = I_g + I_s\)
Substituting for \(I_s\) gives us:
\(I_s = I - I_g\)
The voltage across the ammeter and the shunt resistor must be the same, thus:
\(I_g \cdot R_g = I_s \cdot R_s\)
Substitute \(I_s\) into the equation:
\(R_s = \frac{I_g \cdot R_g}{I - I_g}\)
Substituting the values:
\(R_s = \frac{0.001 \times 100}{1 - 0.001}\)
Calculating this gives:
\(R_s = \frac{0.1}{0.999} \approx 0.1001 \, \Omega\)
Therefore, the required shunt resistance to convert a 1 mA ammeter into a 1 A ammeter is approximately 0.1001 Ω, which matches option (b).
Hence, the correct answer is 0.1001 Ω.
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