In a series R-C circuit supplied with sinusoidal AC voltage, the current leads the applied voltage by an angle φ. Which of the following correctly expresses this phase angle?
Answer & step-by-step solution
Correct answer: C. tan φ = −X_C/R
Quick explanation
The paper uses the signed impedance angle: Z = R − jX_C, so tan φ = −X_C/R. (As a pure magnitude, the current leads by tan⁻¹(X_C/R).)
Z = R − jX_C
tan φ_Z = −X_C / R
|lead angle| = tan⁻¹(X_C / R)
Phase angle of a series R-C circuit
Capacitive reactance lies on the negative imaginary axis, so Z = R − jX_C and tan φ_Z = −X_C/R.
Meaning of the negative sign
The negative impedance angle shows capacitive behaviour. Because I = V/Z, the current leads the voltage by tan⁻¹(X_C/R).
Wording issue in the source
If φ meant only the positive size of the lead, one would write tan φ = X_C/R. The official key treats φ as the signed impedance angle, so option C is the intended answer.
Exam tipA capacitive circuit has a negative impedance angle even though current leads voltage by a positive magnitude.
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