Question
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?
Answer Options
- A) 63 degrees with the voltage lagging the current
- B) 63 degrees with the voltage leading the current
- C) 27 degrees with the voltage leading the current
- D) 27 degrees with the voltage lagging the current
Correct Answer: A
Explanation
The phase angle (\phi) in a series RLC circuit depends on the relative magnitudes of the resistance (R) and the net reactance (X_{net}). The formula is \phi = \arctan(X_{net}/R), where X_{net} = X_L - X_C. Here, R = 100 \Omega, X_L = 100 \Omega, and X_C = 300 \Omega. The net reactance is X_{net} = 100 - 300 = -200 \Omega. The negative sign means the circuit is capacitive.
The phase angle is \phi = \arctan(-200/100) = \arctan(-2) \approx -63.43^\circ. Since the angle is negative, it means the current is leading the voltage, or the voltage is lagging the current by 63 degrees, which is the definitive characteristic of a capacitive circuit (‘ICE man’: current (I) leads voltage (E) in a capacitive circuit (C)).
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