Compute conductance: What is the conductance (in siemens) of an 8 Ω resistor, and which option correctly expresses it in millisiemens (mS)?
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A125 mS
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B12.5 mS
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C12 S
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D8 mS
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E0.125 S
Answer
Correct Answer: 125 mS
Explanation
Introduction / Context:Conductance is the reciprocal of resistance and is useful for parallel circuit analysis, admittance calculations, and AC analysis in complex form. Converting between ohms and siemens is a simple but common task in circuit design and troubleshooting.
Given Data / Assumptions:
- Resistance R = 8 Ω.
- Conductance G is defined as 1 / R.
- 1 siemens (S) = 1000 millisiemens (mS).
Concept / Approach:
Use G = 1 / R for DC conductance. Ensure the final unit presentation is correct and, if required, scale to mS for clarity in typical component value ranges.
Step-by-Step Solution:
Apply the formula: G = 1 / R.Substitute: G = 1 / 8 = 0.125 S.Convert to mS: 0.125 S * 1000 = 125 mS.Therefore, conductance is 0.125 S, which equals 125 mS.Verification / Alternative check:
Check reciprocal: 1 / 0.125 S = 8 Ω, which matches the original resistance, confirming the conversion is correct.
Why Other Options Are Wrong:
12.5 mS corresponds to 80 Ω, not 8 Ω. 12 S corresponds to ≈ 0.083 Ω. 8 mS corresponds to 125 Ω. 0.125 S is numerically correct in siemens but the option asks for millisiemens; the best matching formatted answer is 125 mS.
Common Pitfalls:
Forgetting to multiply by 1000 to convert S to mS; mixing up reciprocal relationships; rounding incorrectly when dealing with fractional siemens values.
Final Answer:
125 mS