AC Source & Phasor
v(t) = V₀ sin(ωt). Rotating phasor projects onto sine wave. V_rms = V₀/√2.
Key Notes
An AC source produces a sinusoidal voltage v(t) = V₀ sin(ωt), where V₀ is the peak amplitude and ω = 2πf is the angular frequency.
Indian mains: 230 V rms, 50 Hz. So V₀ ≈ 325 V and T = 20 ms.
RMS value is the DC-equivalent — the steady DC voltage that would deliver the SAME average power to a resistor.
For a sine wave: V_rms = V₀/√2 ≈ 0.707 V₀.
Phasor representation: V₀ is the length of a vector rotating at ω; its y-projection (or x-projection, by convention) gives the instantaneous value.
The PHASE of an AC source is its angular offset at t = 0 — it sets when the wave 'starts'.
AC waveforms can also be triangular or square, but unless otherwise stated 'AC' means sinusoidal.
Formulas
Instantaneous voltage
ω = 2πf; φ is the phase at t = 0.
RMS voltage
DC-equivalent value for power purposes.
Period and frequency
Time for one full cycle.
Peak-to-peak
Difference between max and min — what oscilloscopes display.
Important Points
When a textbook says '220 V AC' it ALWAYS means rms unless explicitly stated otherwise.
V₀ is what the insulation must withstand, but V_rms is what determines heating and power.
Sine waves are special because their derivative and integral are also sinusoids of the same frequency — that's why phasor algebra works.
Frequency in India = 50 Hz; in USA/Canada = 60 Hz. The choice has no deep physics — it's historical / cost optimisation.
Phase shifts are crucial when comparing two AC quantities (V vs I, or two voltages) — they decide power factor and resonance.
Phasor (V₀, ωt) rotates counter-clockwise by convention.
AC Source & Phasor 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.