Vedatom Physics
Electromagnetism / Alternating Current
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Alternating current — the rules
RMS. A meter never reads the peak. It reports the root-mean-square: Irms = I₀/√2, Vrms = V₀/√2 — the steady DC that would heat a resistor at the same rate. The mean over a cycle is zero; the mean of |i| is 2I₀/π.
Phasors. Draw each voltage and current as a rotating vector; only the angle between them (φ) matters. Add reactive voltages as vectors, never as plain numbers.
Reactance. XL = ωL (V leads I by 90°), XC = 1/ωC (V lags I by 90°), R in phase. Remember CIVIL: in C, I leads V; in L, V leads I.
Impedance & resonance. Z = √R² + (XL−XC)². At ω₀ = 1/√LC the reactances cancel, Z = R is least and I is greatest. Sharpness Q = (1/R)√L/C.
Power. P = VrmsIrms cosφ; cosφ is the power factor. A pure reactance draws current but no average power — the wattless current I sinφ.
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EM Lab · all topics
§01

AC, phasors & the RMS value

A rotating vector — a phasor — spins at ω, and its shadow on the vertical axis is the alternating current: i = I₀ sin ωt. Watch the wheel on the left paint the wave on the right. Its average over a whole cycle is a useless zero, so we quote the rms value I₀/√2 ≈ 0.707 I₀ — the steady DC that would warm a resistor at exactly the same rate. That green band is where the rms sits.

THE PHASOR WHEEL PAINTS THE SINE · i = I₀ sin ωt
+I₀ +I₀/√2 green band = rms · dashed = peak
heating ∝ i² (always ≥ 0) · its mean = I₀²/2 mean → rms = I₀/√2
live i = 0.00 A
peak I₀{{ a1I0lab }}
angular speed ω{{ a1wlab }}
Irms = I₀√2
peak I₀
{{ a1I0lab }}
rms I₀/√2
{{ a1rmslab }}
mean of |i| = 2I₀/π{{ a1meanlab }}
"230 V mains" is the rms. Its peak is 230√2 ≈ 325 V — which is what the insulation must actually survive.
Why √2, not 2?
Heating goes as i², and the average of sin²ωt over a cycle is exactly ½. Take the square root of that mean and the peak drops by √2 — never by 2. Same trick converts peak voltage to Vrms.