What is the capacitance of a 20-microfarad capacitor connected in series with a 50-microfarad capacitor?
The correct answer is B: 14.3 microfarads. The capacitance of a 20-microfarad capacitor connected in series with a 50-microfarad capacitor is 14.3 microfarads. 1/Ctotal = 1/20 + 1/50 = 0.05 + 0.02 = 0.07. Ctotal = 1/0.07 = 14.29 µF ≈ 14.3 µF. For amateur radio operators, this is a basic series capacitance calculation. Understanding this helps when analyzing series capacitors.
Exam Tip
Series capacitance: 1/C = 1/20 + 1/50 = 0.07, C = 1/0.07 = 14.3 µF. Think 'S'eries 'C'apacitors = 'S'um of 'R'eciprocals, then 'R'eciprocal. Use 1/Ctotal = 1/C1 + 1/C2. Not 0.07 µF (reciprocal), not 70 µF (sum), not 1000 µF - just 14.3 µF.
Memory Aid
"Series capacitance: 1/C = 0.07, C = 14.3 µF. Think 'S'eries 'C'apacitors = 'S'um of 'R'eciprocals. Use 1/Ctotal = 1/C1 + 1/C2, then take reciprocal. Standard series calculation."
Real-World Application
Two capacitors in series: 20 µF and 50 µF. 1/Ctotal = 1/20 + 1/50 = 0.05 + 0.02 = 0.07. Ctotal = 1/0.07 = 14.29 microfarads ≈ 14.3 microfarads. Series capacitance is less than either individual capacitor.
Key Concepts
Why Other Options Are Wrong
Option A (0.07 microfarads): Incorrect. 0.07 µF is the reciprocal (1/Ctotal), not the total capacitance. You need to take 1/0.07 = 14.3 µF.
Option C (70 microfarads): Incorrect. 70 µF is the sum (parallel), not series. Series capacitance is less than individual capacitors.
Option D (1,000 microfarads): Incorrect. 1,000 µF is way too high - that would be 20 × 50, not the series combination. Calculation error.
题目解析
The correct answer is B: 14.3 microfarads. The capacitance of a 20-microfarad capacitor connected in series with a 50-microfarad capacitor is 14.3 microfarads. 1/Ctotal = 1/20 + 1/50 = 0.05 + 0.02 = 0.07. Ctotal = 1/0.07 = 14.29 µF ≈ 14.3 µF. For amateur radio operators, this is a basic series capacitance calculation. Understanding this helps when analyzing series capacitors.
考试技巧
Series capacitance: 1/C = 1/20 + 1/50 = 0.07, C = 1/0.07 = 14.3 µF. Think 'S'eries 'C'apacitors = 'S'um of 'R'eciprocals, then 'R'eciprocal. Use 1/Ctotal = 1/C1 + 1/C2. Not 0.07 µF (reciprocal), not 70 µF (sum), not 1000 µF - just 14.3 µF.
记忆口诀
Series capacitance: 1/C = 0.07, C = 14.3 µF. Think 'S'eries 'C'apacitors = 'S'um of 'R'eciprocals. Use 1/Ctotal = 1/C1 + 1/C2, then take reciprocal. Standard series calculation.
实际应用示例
Two capacitors in series: 20 µF and 50 µF. 1/Ctotal = 1/20 + 1/50 = 0.05 + 0.02 = 0.07. Ctotal = 1/0.07 = 14.29 microfarads ≈ 14.3 microfarads. Series capacitance is less than either individual capacitor.
错误选项分析
Option A (0.07 microfarads): Incorrect. 0.07 µF is the reciprocal (1/Ctotal), not the total capacitance. You need to take 1/0.07 = 14.3 µF. Option C (70 microfarads): Incorrect. 70 µF is the sum (parallel), not series. Series capacitance is less than individual capacitors. Option D (1,000 microfarads): Incorrect. 1,000 µF is way too high - that would be 20 × 50, not the series combination. Calculation error.
知识点
Series capacitors, Total capacitance, Reciprocal sum, Series circuit
Verified Content
Question from official FCC General Class question pool. Explanation reviewed by licensed amateur radio operators.