Question
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?
Answer Options
- A) 27 degrees with the voltage lagging the current
- B) 27 degrees with the voltage leading the current
- C) 63 degrees with the voltage lagging the current
- D) 63 degrees with the voltage leading the current
Correct Answer: B
Explanation
The phase angle (\phi) of a series RLC circuit is calculated as \phi = \arctan(X_{net}/R), where X_{net} = X_L - X_C. Here, R = 100 \Omega, X_L = 75 \Omega, and X_C = 25 \Omega. The net reactance is X_{net} = 75 - 25 = +50 \Omega. The positive net reactance indicates that the circuit is predominantly inductive.
The phase angle is \phi = \arctan(+50/100) = \arctan(+0.5) \approx +26.56^\circ. Since the angle is positive, it means the voltage is leading the current, a characteristic of an inductive circuit (‘ELI man’). Therefore, the angle is 27 degrees with the voltage leading the current.
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