What is the phase angle between the voltage across and the current through a series RLC circuit if XC is 500 ohms, R is 1 kilohm, and XL is 250 ohms?
The correct answer is C: 14.0 degrees with the voltage lagging the current. What is the phase angle between the voltage across and the current through a series RLC circuit if XC is 500 ohms, R is 1 kilohm, and XL is 250 ohms is 14.0 degrees with the voltage lagging the current. Net reactance = XL - XC = 250 - 500 = -250 ohms (capacitive). Phase angle = arctan(X/R) = arctan(-250/1000) ≈ -14.0°, so voltage lags current. For amateur radio operators, this is important for circuit calculations. Understanding this helps when calculating phase angles.
Exam Tip
Series RLC phase angle = arctan((XL-XC)/R). Think 'P'hase 'A'ngle = arctan('N'et 'R'eactance/'R'esistance). Net X = 250-500 = -250Ω (capacitive), angle = arctan(-250/1000) ≈ -14.0°, voltage lags. Not 68.2°, not leading - just 14.0° lagging.
Memory Aid
"Series RLC phase angle = arctan((XL-XC)/R). Think 'P'hase 'A'ngle = '1'4.0° lagging. Net X = -250Ω, angle = -14.0°, voltage lags. Important for circuit calculations."
Real-World Application
A series RLC circuit with XC=500Ω, R=1kΩ, XL=250Ω: Net reactance = XL-XC = 250-500 = -250Ω (capacitive). Phase angle = arctan(X/R) = arctan(-250/1000) ≈ -14.0°. Since net reactance is capacitive, voltage lags current. This is the phase angle - 14.0° with voltage lagging current.
Key Concepts
Why Other Options Are Wrong
Option A: Incorrect. 68.2 degrees with voltage leading isn't correct - net reactance is capacitive, so voltage lags. 68.2° leading is wrong.
Option B: Incorrect. 14.0 degrees with voltage leading isn't correct - net reactance is capacitive, so voltage lags. Leading is wrong.
Option D: Incorrect. 68.2 degrees with voltage lagging isn't correct - the angle is 14.0°, not 68.2°. 68.2° is wrong.
题目解析
The correct answer is C: 14.0 degrees with the voltage lagging the current. What is the phase angle between the voltage across and the current through a series RLC circuit if XC is 500 ohms, R is 1 kilohm, and XL is 250 ohms is 14.0 degrees with the voltage lagging the current. Net reactance = XL - XC = 250 - 500 = -250 ohms (capacitive). Phase angle = arctan(X/R) = arctan(-250/1000) ≈ -14.0°, so voltage lags current. For amateur radio operators, this is important for circuit calculations. Understanding this helps when calculating phase angles.
考试技巧
Series RLC phase angle = arctan((XL-XC)/R). Think 'P'hase 'A'ngle = arctan('N'et 'R'eactance/'R'esistance). Net X = 250-500 = -250Ω (capacitive), angle = arctan(-250/1000) ≈ -14.0°, voltage lags. Not 68.2°, not leading - just 14.0° lagging.
记忆口诀
Series RLC phase angle = arctan((XL-XC)/R). Think 'P'hase 'A'ngle = '1'4.0° lagging. Net X = -250Ω, angle = -14.0°, voltage lags. Important for circuit calculations.
实际应用示例
A series RLC circuit with XC=500Ω, R=1kΩ, XL=250Ω: Net reactance = XL-XC = 250-500 = -250Ω (capacitive). Phase angle = arctan(X/R) = arctan(-250/1000) ≈ -14.0°. Since net reactance is capacitive, voltage lags current. This is the phase angle - 14.0° with voltage lagging current.
错误选项分析
Option A: Incorrect. 68.2 degrees with voltage leading isn't correct - net reactance is capacitive, so voltage lags. 68.2° leading is wrong. Option B: Incorrect. 14.0 degrees with voltage leading isn't correct - net reactance is capacitive, so voltage lags. Leading is wrong. Option D: Incorrect. 68.2 degrees with voltage lagging isn't correct - the angle is 14.0°, not 68.2°. 68.2° is wrong.
知识点
Phase angle, Voltage across, Current through, Series RLC circuit, XC 500 ohms, R 1 kilohm, XL 250 ohms, 14.0 degrees, Voltage lagging current
Verified Content
Question from official FCC Extra Class question pool. Explanation reviewed by licensed amateur radio operators.