Power components in an RL circuit For a sinusoidal source feeding a series resistor–inductor (RL) network, is the delivered power composed of both real (resistive) and reactive (inductive) components?

Introduction / Context:AC power in reactive circuits splits into real power (converted to heat or useful work) and reactive power (alternately stored and released by fields). An RL circuit includes both a resistor and an inductor, so it naturally involves both components.

Given Data / Assumptions:

• Series RL under sinusoidal steady state.
• Real power consumed by R; reactive power exchanged by L.
• Voltage and current may be out of phase by angle phi, where tan(phi) = XL / R.

Concept / Approach:

Instantaneous power fluctuates over a cycle, but average real power over one cycle is P = V_rms * I_rms * cos(phi). The reactive component is Q = V_rms * I_rms * sin(phi), associated with energy stored in and returned from the inductor's magnetic field. Apparent power is S = V_rms * I_rms, with S^2 = P^2 + Q^2.

Step-by-Step Solution:

Verification / Alternative check:

Power factor PF = cos(phi) is less than 1 whenever XL > 0, proving that some of the apparent power is reactive. Measuring input and load waveforms with a wattmeter and a VAR meter confirms nonzero P and Q.

Why Other Options Are Wrong:

• “Only real power” ignores the inductor’s energy storage.
• “Only reactive power” ignores resistive heating in R.
• “Reactive power appears only at resonance” is incorrect; resonance applies to RLC, not a simple RL, and reactive power exists for any XL > 0.

Common Pitfalls:

Assuming P + Q addition without using RMS and phase relationships. Always calculate with RMS quantities and the phase angle between voltage and current.

Final Answer:

True