Deep Dive: E5B08
The correct answer is A: 63 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 300 ohms, R is 100 ohms, and XL is 100 ohms is 63 degrees with the voltage lagging the current. Net reactance = XL - XC = 100 - 300 = -200 ohms (capacitive). Phase angle = arctan(X/R) = arctan(-200/100) = arctan(-2) ≈ -63°, so voltage lags current. For amateur radio operators, this is important for circuit calculations. Understanding this helps when calculating phase angles.
Why Other Answers Are Wrong
Option B: Incorrect. 63 degrees with voltage leading isn't correct - net reactance is capacitive, so voltage lags. Leading is wrong. Option C: Incorrect. 27 degrees with voltage leading isn't correct - net reactance is capacitive, so voltage lags, and angle is 63°, not 27°. 27° leading is wrong. Option D: Incorrect. 27 degrees with voltage lagging isn't correct - the angle is 63°, not 27°. 27° is wrong.
Exam Tip
Series RLC phase angle = arctan((XL-XC)/R). Think 'P'hase 'A'ngle = arctan('N'et 'R'eactance/'R'esistance). Net X = 100-300 = -200Ω (capacitive), angle = arctan(-200/100) = arctan(-2) ≈ -63°, voltage lags. Not leading, not 27° - just 63° lagging.
Memory Aid
Series RLC phase angle = arctan((XL-XC)/R). Think 'P'hase 'A'ngle = '6'3° lagging. Net X = -200Ω, angle = -63°, voltage lags. Important for circuit calculations.
Real-World Example
A series RLC circuit with XC=300Ω, R=100Ω, XL=100Ω: Net reactance = XL-XC = 100-300 = -200Ω (capacitive). Phase angle = arctan(X/R) = arctan(-200/100) = arctan(-2) ≈ -63°. Since net reactance is capacitive, voltage lags current. This is the phase angle - 63° with voltage lagging current.
Source & Coverage
Question Pool: 2024-2028 Question Pool
Subelement: E5B
Reference: 2024-2028 Question Pool · E5 - Electrical Principles
Key Concepts
Verified Content
Question from the official FCC Extra Class pool. Explanation reviewed by licensed amateur radio operators and mapped to the E5B topic.