RMS Values
V_rms = V₀/√2 — DC equivalent for power. Mains 230 V is RMS, peak 325 V.
Key Notes
Root-mean-square (rms) value of an AC quantity is the DC equivalent that delivers the SAME average power to a resistor.
For sinusoidal AC: V_rms = V₀/√2 and I_rms = I₀/√2.
Mean voltage over a full sine cycle is ZERO (positive and negative halves cancel) — that's why ⟨V²⟩ is used.
Average power: P_avg = V_rms·I_rms = V_rms²/R = I_rms²·R (matches DC form).
rms is what AC meters display by default. '230 V mains' means 230 V rms.
Average over a half-cycle (magnitude only): |V|_avg = 2V₀/π ≈ 0.637 V₀ — DIFFERENT from rms.
For NON-sinusoidal waveforms: rms must be computed from the specific waveform. For a square wave amplitude V₀: V_rms = V₀ (no factor of √2).
Formulas
rms (sinusoidal)
From ⟨sin²⟩ = ½ over a full cycle.
Magnitude-average (half-cycle)
Average of |sin| from 0 to π.
Average power in R
DC-equivalent power.
Square wave rms
No factor of √2 — flat amplitude.
Triangular wave rms
Different factor for different waveform shapes.
Important Points
rms ≠ average. Mean of sin over a full cycle is ZERO; rms is V₀/√2.
rms is the DC equivalent for power. Same V_rms means same heating in a resistor.
Indian mains: 230 V rms → V₀ ≈ 325 V. Insulation must handle this peak.
Power-rating of appliances is in W or kW — assumes rms values.
Different waveforms have different rms factors — only sinusoidal gives V₀/√2.
Common mistake: using V₀ instead of V_rms in P = V²/R. Always use rms unless explicitly told peak.
RMS Values 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.