Power factor: where does the power go?
"Power factor: where does the power go?" is a free, interactive Class 12 Physics simulation for NEET and JEE, built on the NCERT section "Power factor" in Alternating Current. V, i and p = vi over two cycles for a chosen phase angle, positive and negative areas of p shaded, and the average VI cos φ marked. NEET has asked about this idea 2 times in 10 years of papers. JEE Main asked 37 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
From the lesson Power factor in Alternating Current. Change the values and watch what happens.
What it shows
NCERT §7.7
V, i and p = vi over two cycles for a chosen phase angle, positive and negative areas of p shaded, and the average VI cos φ marked.
Controls
3 to try
- Sliderphase φ −90° to +90°
- Sliderrms current 0–10 A
- supply fixed at 220 V rms
Try this
Find the phase at which a 5 A current draws zero average power (±90°), then the phase giving power factor 0.6 (53.1°)
Common mistake
Assuming no current flows when no power is used (wattless current)
In NEET
10 years of papers
Asked 2 times in 10 years of NEET.
See the past questions: LCR Circuits, Alternating Current (chapter)
In JEE Main
42 shifts analysed
37 questions from Alternating Current across the 42 JEE Main shifts Lumi has analysed (2017–2026).
The idea behind it
NCERT §7.7
- With v = vm sin ωt and i = im sin(ωt + φ), the average power over a cycle is P = (vm im/2) cos φ = VI cos φ. It can also be written P = I²Z cos φ.
- cos φ is the power factor. The power depends on the phase angle as well as on V and I.
- Purely resistive circuit: φ = 0, cos φ = 1, and the power is the largest possible for that V and I.
- Pure L or pure C: φ = π/2, cos φ = 0, and no power is used even though current flows. Such a current is called wattless current.
- In any LCR circuit, power is used up only in the resistor. At resonance φ = 0, cos φ = 1 and P = I²R, the most power for the circuit.
- Example 7.7: for a given power at a given voltage, a low power factor means a bigger current and so bigger I²R loss in the lines. A lagging wattless current can be cancelled by a capacitor connected in parallel, which raises the power factor towards 1.
- Example 7.8: peak 283 V at 50 Hz on R = 3 Ω, L = 25.48 mH, C = 796 μF. XL = 8 Ω, XC = 4 Ω, Z = 5 Ω, φ = −53.1° (current lags), I = 40 A, P = 4800 W and power factor 0.6.
- Example 7.9: the same circuit resonates at ω₀ = 1/√(LC), about 222 rad/s or 35.3 Hz. There Z = R = 3 Ω, the rms current is 66.7 A and the power is 13.35 kW, more than at 50 Hz.
Questions
5 answers
- What does the "Power factor: where does the power go?" simulation show?
- V, i and p = vi over two cycles for a chosen phase angle, positive and negative areas of p shaded, and the average VI cos φ marked.
- What mistake does the "Power factor: where does the power go?" simulation fix?
- A common mistake it clears up: assuming no current flows when no power is used (wattless current)
- Has NEET asked about this idea?
- Yes. NEET has asked about this idea 2 times in 10 years of papers.
- Does JEE Main ask questions from Alternating Current?
- Yes. JEE Main asked 37 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
- Is this simulation free?
- Yes. It is free and runs in the browser on a phone or a laptop. It belongs to the lesson "Power factor" in Alternating Current (Class 12 Physics).
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