AC through Resistor
I in phase with V (φ = 0°). I₀ = V₀/R.
Key Notes
When AC voltage v = V₀ sin(ωt) drives a pure resistor R, the current is i = (V₀/R) sin(ωt).
V and I are IN PHASE — they peak, zero, and reverse together. Phase angle φ = 0.
Peak current: I₀ = V₀/R. RMS current: I_rms = V_rms/R = I₀/√2.
Average power: P_avg = V_rms · I_rms = V_rms²/R = I_rms²·R — exactly like a DC formula but with rms values.
Resistors dissipate energy continuously — instantaneous power p(t) = v·i = (V₀²/R) sin²(ωt) ≥ 0.
On a phasor diagram, V and I phasors point in the SAME direction.
Resistors do not store energy; they dissipate it as heat (Joule heating).
Formulas
Current
Same shape and phase as the voltage; amplitude scaled by 1/R.
Peak / rms values
Both relate by I₀ = √2 · I_rms.
Average power
Same form as DC — power factor cosφ = 1.
Instantaneous power
Always ≥ 0; average = V₀I₀/2 = V_rms·I_rms.
Important Points
A pure resistor in AC behaves IDENTICALLY to a resistor in DC — only the values are rms.
Power dissipated is positive throughout the cycle — energy always flows source → resistor.
Power oscillates at TWICE the source frequency (because of sin²).
Phase φ = 0 ⇒ power factor cos φ = 1 ⇒ full power delivered.
Resistors are the 'simple' element — they introduce no phase shift, no energy storage.
In LCR series circuits, the R branch is the only one that DISSIPATES energy; L and C only store/return it.
AC through Resistor 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.