Power & Power Factor
P_avg = V_rms·I_rms·cosφ. Watch p(t) = v·i and the average line.
Key Notes
Instantaneous power in an AC circuit: p(t) = v(t)·i(t). For sinusoidal v and i with phase difference φ: p(t) varies, but ITS AVERAGE matters.
Average power: P_avg = V_rms · I_rms · cos φ. The factor cos φ is called the POWER FACTOR.
Pure R: cos φ = 1 ⇒ full power delivered.
Pure L or C: cos φ = 0 ⇒ no power dissipated (wattless current — energy oscillates but doesn't transfer net).
Mixed circuit: cos φ = R/Z. Higher reactance ⇒ smaller cos φ ⇒ less real power for same current.
Real power (W) vs apparent power (VA): P = V_rms·I_rms·cos φ (real), S = V_rms·I_rms (apparent). Reactive power Q = V_rms·I_rms·sin φ (VAR).
Power factor correction: industries add capacitors in parallel with inductive loads to bring cos φ close to 1. Lowers I for the same P → reduces transmission losses.
Formulas
Average (real) power
Energy actually consumed per unit time.
Instantaneous power
Includes both flowing and oscillating components.
Apparent power
What the circuit appears to draw — measured in volt-amperes (VA).
Reactive power
Energy that oscillates between source and reactive components (VAR).
Power factor
Ratio of real to apparent power.
Important Points
Power dissipates ONLY in R. L and C just shuffle energy back and forth.
Cos φ = 1 is ideal (purely resistive). For motors, cos φ ≈ 0.7–0.85 — industries pay penalties if too low.
Real power (W) and reactive power (VAR) are perpendicular components; apparent power (VA) is their vector magnitude.
Same kW load at lower power factor draws MORE current — more I²R losses in transmission lines.
'Wattless current' = current flowing with no net power transfer. Happens in pure L or pure C.
Common pitfall: forgetting cos φ. P ≠ V_rms × I_rms unless circuit is purely resistive.
Power & Power Factor notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.