“ELI the ICE man”
Who leads, voltage or current
In an inductor (L), E leads I: ELI. In a capacitor (C), I leads E: ICE. One phrase settles every phase question in the chapter.
Class 12 Physics · Gujarat Board, CBSE, GUJCET, JEE and NEET
Alternating Current formulas
AC takes the DC circuit you already know and adds phase. Reactance replaces resistance for capacitors and inductors, impedance ties them together, and resonance is the one result asked every single year.
15 formulas, 3 memory hooks, and the 5 mistakes that cost the most marks.
RMS and average
| What | Formula | Symbols and notes |
|---|---|---|
| RMS current | Irms = I₀/√2 = 0.707I₀ | what an AC ammeter reads |
| RMS voltage | Vrms = V₀/√2 | 230 V mains means a peak of about 325 V |
| Average over a full cycle | zero | which is why RMS values are used at all |
| Angular frequency | ω = 2πf | f is 50 Hz in India |
Reactance and impedance
| What | Formula | Symbols and notes |
|---|---|---|
| Inductive reactance | XL = ωL = 2πfL | rises with frequency; an inductor blocks high frequency |
| Capacitive reactance | XC = 1/ωC = 1/2πfC | falls with frequency; a capacitor blocks DC |
| Impedance of a series LCR | Z = √(R² + (XL − XC)²) | the AC version of resistance |
| Phase angle | tanφ = (XL − XC)/R | current lags when inductive, leads when capacitive |
| Current | Irms = Vrms/Z | Ohm's law with impedance in place of resistance |
Power and resonance
| What | Formula | Symbols and notes |
|---|---|---|
| Average power | P = VrmsIrms cosφ | cosφ is the power factor |
| Power factor | cosφ = R/Z | one for a pure resistor, zero for a pure inductor or capacitor |
| Wattless current | P = 0 when φ = 90° | a pure inductor or capacitor consumes no average power |
| Resonant frequency | f₀ = 1/2π√(LC) | at resonance XL = XC |
| At resonance | Z = R, current is maximum, φ = 0 | the circuit behaves as a pure resistor |
| Quality factor | Q = (1/R)√(L/C) | sharper resonance means a higher Q |
Taught by Darshit Bhatt, founder and lead faculty at Darshit Sir Institute. Instrumentation and Control engineer, with a master's degree and a chartered degree, teaching in Paldi, Ahmedabad since 2006.
Know the formula but not when to use it?
Darshit Sir has taught this in Paldi since 2006, in the classroom and live online.
Memory hooks
How to remember this chapter.
“Inductors hate fast, capacitors hate slow”
How reactance changes with frequency
XL rises with frequency and XC falls. That is why a capacitor blocks DC completely and an inductor passes it freely.
“Resonance is a tie”
What happens at f₀
The two reactances cancel exactly, impedance drops to R, and the current peaks. It is how a radio picks one station out of many.
Where marks go
The mistakes that cost the most.
- Using peak values where RMS is meant. Meters read RMS, and the mains 230 V is RMS.
- Adding the reactances to the resistance directly. They are at 90°, so they combine as a right triangle.
- Forgetting the power factor. Without cosφ the power is wrong for every circuit except a pure resistor.
- Thinking a capacitor or inductor consumes power. Over a full cycle they consume none.
- Believing the voltage across L can never exceed the source voltage. At resonance it can, and by a large factor.
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