Phase Difference and Average Power
For sinusoidal steady state, average real power is Vrms Irms cos(phi). The factor cos(phi) is the power factor.
Why this shows up in the exam
Electricity billing · Motor power-factor correction · Sizing transmission equipment
Learn the idea
Only the in-phase part of current consumes average power. Voltage and current can peak at different times. The current component aligned with voltage transfers net energy to the circuit; the quadrature component gives energy back.
🧠 Memory hook: Power follows the in-phase current.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- P_avg = V_rms I_rms cos(phi) — real average power
- power factor = cos(phi) = R/Z — series circuit power factor
How to approach it
- 1Find the phase difference
- 2Use RMS values
- 3Apply cos(phi) with the correct sign
Common slip-ups that cost marks
- •Multiplying peak V and peak I directly
- •Using sin(phi) for real power
- •Calling reactive power consumed energy
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A conducting rod of length 2 m moves at 3 m/s perpendicular to a 4 T magnetic field. Find the motional emf.
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