For an RL circuit, the phase angle is always ________

Question

Examoogle · Accepted Answer

Negative

Explanation: In an RL series circuit, the current lags the voltage by a phase angle $\phi$. By convention, when the current lags the voltage, the phase angle is positive, as $\phi = \arctan(\frac{X_L}{R})$.

Working Principle: The inductor opposes changes in current, causing the current to reach its peak value after the voltage peak. The impedance is complex, given by $Z = R + jX_L$. The phase angle is defined as the argument of the complex impedance, which is $	heta = 	an^{-1}(\frac{\omega L}{R})$. Since $R$ and $X_L$ are positive in passive circuits, the angle is positive, leading to a lagging power factor.

Key Formulas: $\phi = \arctan(\frac{X_L}{R})$ — Phase angle formula; $Z = \sqrt{R^2 + X_L^2} \angle \phi$ — Impedance in polar form

Key Points: In an RL circuit, voltage leads the current.; The phase angle $\phi$ is defined relative to the current; since current lags, the angle is typically expressed as positive when referring to the lead of voltage over current.; The power factor is $\cos(\phi)$, which is lagging for RL circuits.

Advantages: Used in filtering applications; Used in induction motors and transformers

Disadvantages: Introduces lagging power factor; Causes voltage drops in distribution lines

Applications: Induction motors; Magnetic ballasts for lighting

Additional Info: Note: The provided question states the answer is Negative, which is a common point of confusion in sign conventions. In standard engineering practice, the phase angle of the impedance of an RL circuit is positive, leading to a lagging current.. If the question defines the phase angle of current with respect to voltage, it is often denoted as $-\phi$.

Answer: B is correct — In standard AC analysis, the impedance of an RL circuit has a positive phase angle, causing current to lag voltage.

Exam Tip: Always remember: ELI the ICE man. In an Inductor (L), E (Voltage) leads I (Current); in a Capacitor (C), I leads E.

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