What is the capacitance of three 100-microfarad capacitors connected in series?
The correct answer is C: 33.3 microfarads. The capacitance of three 100-microfarad capacitors connected in series is 33.3 microfarads. 1/Ctotal = 1/100 + 1/100 + 1/100 = 3/100 = 0.03. Ctotal = 1/0.03 = 33.3 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 = 1/100 + 1/100 + 1/100 = 3/100 = 0.03, C = 1/0.03 = 33.3 µF. Think 'S'eries 'C'apacitors = 'S'um of 'R'eciprocals, then 'R'eciprocal. Use 1/Ctotal = 1/C1 + 1/C2 + 1/C3. Not 0.33 µF, not 3.0 µF, not 300 µF (sum) - just 33.3 µF.
Memory Aid
"Series capacitance: 1/C = 3/100 = 0.03, C = 33.3 µF. Think 'S'eries 'C'apacitors = 'S'um of 'R'eciprocals. Use 1/Ctotal = 1/C1 + 1/C2 + 1/C3, then take reciprocal. Standard series calculation."
Real-World Application
Three capacitors in series: 100 µF each. 1/Ctotal = 1/100 + 1/100 + 1/100 = 3/100 = 0.03. Ctotal = 1/0.03 = 33.3 microfarads. Series capacitance is less than individual capacitors (33.3 < 100).
Key Concepts
Why Other Options Are Wrong
Option A (0.33 microfarads): Incorrect. 0.33 µF is too low - that would be if capacitance was divided by 300, not 3. Calculation error.
Option B (3.0 microfarads): Incorrect. 3.0 µF is too low - series capacitance is less than individual, but 100/3 = 33.3, not 3.0. Calculation error.
Option D (300 microfarads): Incorrect. 300 µF is the sum (parallel), not series. Series capacitance is less than individual capacitors.
题目解析
The correct answer is C: 33.3 microfarads. The capacitance of three 100-microfarad capacitors connected in series is 33.3 microfarads. 1/Ctotal = 1/100 + 1/100 + 1/100 = 3/100 = 0.03. Ctotal = 1/0.03 = 33.3 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 = 1/100 + 1/100 + 1/100 = 3/100 = 0.03, C = 1/0.03 = 33.3 µF. Think 'S'eries 'C'apacitors = 'S'um of 'R'eciprocals, then 'R'eciprocal. Use 1/Ctotal = 1/C1 + 1/C2 + 1/C3. Not 0.33 µF, not 3.0 µF, not 300 µF (sum) - just 33.3 µF.
记忆口诀
Series capacitance: 1/C = 3/100 = 0.03, C = 33.3 µF. Think 'S'eries 'C'apacitors = 'S'um of 'R'eciprocals. Use 1/Ctotal = 1/C1 + 1/C2 + 1/C3, then take reciprocal. Standard series calculation.
实际应用示例
Three capacitors in series: 100 µF each. 1/Ctotal = 1/100 + 1/100 + 1/100 = 3/100 = 0.03. Ctotal = 1/0.03 = 33.3 microfarads. Series capacitance is less than individual capacitors (33.3 < 100).
错误选项分析
Option A (0.33 microfarads): Incorrect. 0.33 µF is too low - that would be if capacitance was divided by 300, not 3. Calculation error. Option B (3.0 microfarads): Incorrect. 3.0 µF is too low - series capacitance is less than individual, but 100/3 = 33.3, not 3.0. Calculation error. Option D (300 microfarads): Incorrect. 300 µF is the sum (parallel), not series. Series capacitance is less than individual capacitors.
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.