Question
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?
Answer Options
- A) 68.2 degrees with the voltage leading the current
- B) 14.0 degrees with the voltage leading the current
- C) 14.0 degrees with the voltage lagging the current
- D) 68.2 degrees with the voltage lagging the current
Correct Answer: C
Explanation
The phase angle (\phi) of a series RLC circuit is determined by the ratio of the net reactance (X_{net}) to the resistance (R), using the formula \phi = \arctan(X_{net}/R). The net reactance is X_{net} = X_L - X_C. Here, R = 1000 \Omega, X_L = 250 \Omega, and X_C = 500 \Omega. The net reactance is X_{net} = 250 - 500 = -250 \Omega. The negative sign indicates that the circuit is predominantly capacitive.
The phase angle is \phi = \arctan(-250/1000) = \arctan(-0.25) \approx -14.04^\circ. The negative phase angle means the voltage is behind the current, a characteristic of a capacitive circuit. Therefore, the angle is 14.0 degrees with the voltage lagging the current (or current leading the voltage).
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