What is the total resistance of a 10-, a 20-, and a 50-ohm resistor connected in parallel?
The correct answer is A: 5.9 ohms. The total resistance of 10-, 20-, and 50-ohm resistors connected in parallel is 5.9 ohms. 1/Rtotal = 1/10 + 1/20 + 1/50 = 0.1 + 0.05 + 0.02 = 0.17. Rtotal = 1/0.17 = 5.88Ω ≈ 5.9Ω. For amateur radio operators, this is a basic parallel resistance calculation. Understanding this helps when analyzing parallel circuits.
Exam Tip
Parallel resistance: 1/R = 1/10 + 1/20 + 1/50 = 0.17, R = 1/0.17 = 5.9Ω. Think 'P'arallel 'R'esistance = 'P'reciprocal sum, then 'R'eciprocal. Use 1/Rtotal = 1/R1 + 1/R2 + 1/R3. Not 0.17Ω (reciprocal), not 17Ω, not 80Ω (sum) - just 5.9Ω.
Memory Aid
"Parallel resistance: 1/R = 1/10 + 1/20 + 1/50 = 0.17, R = 5.9Ω. Think 'P'arallel 'R'esistance = 'P'reciprocal sum. Use 1/Rtotal = 1/R1 + 1/R2 + 1/R3, then take reciprocal. Standard parallel calculation."
Real-World Application
Three resistors in parallel: 10Ω, 20Ω, and 50Ω. 1/Rtotal = 1/10 + 1/20 + 1/50 = 0.1 + 0.05 + 0.02 = 0.17. Rtotal = 1/0.17 = 5.88 ohms ≈ 5.9 ohms. Parallel resistance is less than the smallest resistor (10Ω).
Key Concepts
Why Other Options Are Wrong
Option B (0.17 ohms): Incorrect. 0.17 ohms is the reciprocal (1/Rtotal), not the total resistance. You need to take 1/0.17 = 5.9Ω.
Option C (17 ohms): Incorrect. 17 ohms is too high - parallel resistance is less than the smallest resistor (10Ω). Calculation error.
Option D (80 ohms): Incorrect. 80 ohms is the sum (series), not parallel. Parallel resistance is less than the smallest resistor.
题目解析
The correct answer is A: 5.9 ohms. The total resistance of 10-, 20-, and 50-ohm resistors connected in parallel is 5.9 ohms. 1/Rtotal = 1/10 + 1/20 + 1/50 = 0.1 + 0.05 + 0.02 = 0.17. Rtotal = 1/0.17 = 5.88Ω ≈ 5.9Ω. For amateur radio operators, this is a basic parallel resistance calculation. Understanding this helps when analyzing parallel circuits.
考试技巧
Parallel resistance: 1/R = 1/10 + 1/20 + 1/50 = 0.17, R = 1/0.17 = 5.9Ω. Think 'P'arallel 'R'esistance = 'P'reciprocal sum, then 'R'eciprocal. Use 1/Rtotal = 1/R1 + 1/R2 + 1/R3. Not 0.17Ω (reciprocal), not 17Ω, not 80Ω (sum) - just 5.9Ω.
记忆口诀
Parallel resistance: 1/R = 1/10 + 1/20 + 1/50 = 0.17, R = 5.9Ω. Think 'P'arallel 'R'esistance = 'P'reciprocal sum. Use 1/Rtotal = 1/R1 + 1/R2 + 1/R3, then take reciprocal. Standard parallel calculation.
实际应用示例
Three resistors in parallel: 10Ω, 20Ω, and 50Ω. 1/Rtotal = 1/10 + 1/20 + 1/50 = 0.1 + 0.05 + 0.02 = 0.17. Rtotal = 1/0.17 = 5.88 ohms ≈ 5.9 ohms. Parallel resistance is less than the smallest resistor (10Ω).
错误选项分析
Option B (0.17 ohms): Incorrect. 0.17 ohms is the reciprocal (1/Rtotal), not the total resistance. You need to take 1/0.17 = 5.9Ω. Option C (17 ohms): Incorrect. 17 ohms is too high - parallel resistance is less than the smallest resistor (10Ω). Calculation error. Option D (80 ohms): Incorrect. 80 ohms is the sum (series), not parallel. Parallel resistance is less than the smallest resistor.
知识点
Parallel resistors, Total resistance, Reciprocal sum, Parallel circuit
Verified Content
Question from official FCC General Class question pool. Explanation reviewed by licensed amateur radio operators.