What is the phase angle between the voltage across and the current through a series RLC circuit if XC is 25 ohms, R is 100 ohms, and XL is 75 ohms?
The correct answer is B: 27 degrees with the voltage leading the current. What is the phase angle between the voltage across and the current through a series RLC circuit if XC is 25 ohms, R is 100 ohms, and XL is 75 ohms is 27 degrees with the voltage leading the current. Net reactance = XL - XC = 75 - 25 = 50 ohms (inductive). Phase angle = arctan(X/R) = arctan(50/100) = arctan(0.5) ≈ 27°, so voltage leads 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 = 75-25 = 50Ω (inductive), angle = arctan(50/100) = arctan(0.5) ≈ 27°, voltage leads. Not lagging, not 63° - just 27° leading.
Memory Aid
"Series RLC phase angle = arctan((XL-XC)/R). Think 'P'hase 'A'ngle = '2'7° leading. Net X = 50Ω, angle = 27°, voltage leads. Important for circuit calculations."
Real-World Application
A series RLC circuit with XC=25Ω, R=100Ω, XL=75Ω: Net reactance = XL-XC = 75-25 = 50Ω (inductive). Phase angle = arctan(X/R) = arctan(50/100) = arctan(0.5) ≈ 27°. Since net reactance is inductive, voltage leads current. This is the phase angle - 27° with voltage leading current.
Key Concepts
Why Other Options Are Wrong
Option A: Incorrect. 27 degrees with voltage lagging isn't correct - net reactance is inductive, so voltage leads. Lagging is wrong.
Option C: Incorrect. 63 degrees with voltage lagging isn't correct - net reactance is inductive, so voltage leads, and angle is 27°, not 63°. 63° lagging is wrong.
Option D: Incorrect. 63 degrees with voltage leading isn't correct - the angle is 27°, not 63°. 63° is wrong.
题目解析
The correct answer is B: 27 degrees with the voltage leading the current. What is the phase angle between the voltage across and the current through a series RLC circuit if XC is 25 ohms, R is 100 ohms, and XL is 75 ohms is 27 degrees with the voltage leading the current. Net reactance = XL - XC = 75 - 25 = 50 ohms (inductive). Phase angle = arctan(X/R) = arctan(50/100) = arctan(0.5) ≈ 27°, so voltage leads 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 = 75-25 = 50Ω (inductive), angle = arctan(50/100) = arctan(0.5) ≈ 27°, voltage leads. Not lagging, not 63° - just 27° leading.
记忆口诀
Series RLC phase angle = arctan((XL-XC)/R). Think 'P'hase 'A'ngle = '2'7° leading. Net X = 50Ω, angle = 27°, voltage leads. Important for circuit calculations.
实际应用示例
A series RLC circuit with XC=25Ω, R=100Ω, XL=75Ω: Net reactance = XL-XC = 75-25 = 50Ω (inductive). Phase angle = arctan(X/R) = arctan(50/100) = arctan(0.5) ≈ 27°. Since net reactance is inductive, voltage leads current. This is the phase angle - 27° with voltage leading current.
错误选项分析
Option A: Incorrect. 27 degrees with voltage lagging isn't correct - net reactance is inductive, so voltage leads. Lagging is wrong. Option C: Incorrect. 63 degrees with voltage lagging isn't correct - net reactance is inductive, so voltage leads, and angle is 27°, not 63°. 63° lagging is wrong. Option D: Incorrect. 63 degrees with voltage leading isn't correct - the angle is 27°, not 63°. 63° is wrong.
知识点
Phase angle, Voltage across, Current through, Series RLC circuit, XC 25 ohms, R 100 ohms, XL 75 ohms, 27 degrees, Voltage leading current
Verified Content
Question from official FCC Extra Class question pool. Explanation reviewed by licensed amateur radio operators.