Alternating Current covers how current and voltage that reverse direction periodically behave in circuits, starting from peak, rms and average values and how resistors, inductors and capacitors each oppose AC through resistance and reactance. It then builds to the series LCR circuit, impedance, resonance and quality factor, AC power and power factor, and applications like transformers and LC oscillations. It is a high-yield, mostly numerical chapter in the NEET Physics syllabus, so mastering rms, reactance, impedance and resonance formulas reliably earns marks.
Key Concepts
1. Alternating Current Basics
An alternating current changes direction periodically. It is described as:
I = I₀ sin ωt and V = V₀ sin ωt
where I₀, V₀ are peak values and ω = 2πf (angular frequency).
RMS (Root Mean Square) Values
The effective or DC-equivalent values used for AC calculations:
Irms = I₀/√2 ≈ 0.707 I₀
Vrms = V₀/√2 ≈ 0.707 V₀
Household AC: Vrms = 220 V → V₀ = 220√2 ≈ 311 V
2. AC Through Pure Components
| Component | Impedance | Phase Relation |
|---|---|---|
| Resistor (R) | R | V and I are in phase |
| Inductor (L) | XL = ωL = 2πfL | V leads I by 90° (π/2) |
| Capacitor (C) | XC = 1/(ωC) = 1/(2πfC) | I leads V by 90° (π/2) |
XL = inductive reactance; XC = capacitive reactance (both in Ω)
3. Series LCR Circuit
Impedance: Z = √[R² + (XL − XC)²]
Current: I = V/Z
Phase angle: tan φ = (XL − XC)/R
- If XL > XC: circuit is inductive (V leads I)
- If XC > XL: circuit is capacitive (I leads V)
- If XL = XC: resonance (purely resistive)
Resonance
At resonance: XL = XC → ωL = 1/(ωC)
Resonant frequency: f₀ = 1/(2π√LC)
At resonance: Z = R (minimum impedance), I = V/R (maximum current)
Quality Factor (Q)
Q = ωL/R = 1/(ωCR) = (1/R)√(L/C)
Higher Q → sharper resonance peak → more selective tuning
4. Power in AC Circuits
P = VrmsIrms cos φ
where cos φ is the power factor.
| Circuit | Power Factor | Power |
|---|---|---|
| Pure R | cos φ = 1 | P = VI (maximum) |
| Pure L or C | cos φ = 0 | P = 0 (wattless current) |
| LCR at resonance | cos φ = 1 | P = V²/R (maximum) |
5. Transformer
A device that changes AC voltage from one level to another using mutual induction.
Vs/Vp = Ns/Np = Ip/Is (for ideal transformer)
- Step-up: Ns > Np → voltage increases, current decreases
- Step-down: Ns < Np → voltage decreases, current increases
- Efficiency: η = (output power)/(input power) × 100%. Ideal transformer: η = 100%
Energy Losses in Transformer
- Copper loss: I²R heating in coils → use thick copper wires
- Iron/core loss: Eddy currents in core → use laminated core
- Hysteresis loss: Energy to magnetise/demagnetise core each cycle → use soft iron
- Flux leakage: Not all flux links both coils → use close winding
Solved Examples
Example 1
A series LCR circuit has R = 100 Ω, L = 0.5 H, C = 10 μF connected to 200 V, 50 Hz. Find impedance and current.
Answer: XL = 2π × 50 × 0.5 = 157 Ω. XC = 1/(2π × 50 × 10⁻⁵) = 318 Ω.
Z = √[100² + (157 − 318)²] = √[10000 + 25921] = √35921 = 189.5 Ω
I = V/Z = 200/189.5 = 1.06 A
Example 2
Find the resonant frequency for L = 0.1 H and C = 100 μF.
Answer: f₀ = 1/(2π√LC) = 1/(2π√(0.1 × 10⁻⁴)) = 1/(2π × 3.16 × 10⁻³) = 50.3 Hz
Example 3
A transformer with 500 primary turns and 50 secondary turns is connected to 220 V AC. Find the output voltage.
Answer: Vs = Vp × Ns/Np = 220 × 50/500 = 22 V (step-down)
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Important Questions for Board Exams
1-Mark
- What is the power factor of a pure inductor?
- What is resonance in an LCR circuit?
3-Mark
- Derive the expression for impedance of a series LCR circuit.
- What is a transformer? Explain its working with a diagram.
- What is resonance? Derive the condition and resonant frequency for a series LCR circuit.
5-Mark
- Explain the working of a series LCR circuit. Derive expressions for impedance and resonant frequency. What is the Q factor?
Quick Revision Points
- AC: I = I₀ sin ωt; Irms = I₀/√2; Vrms = V₀/√2
- XL = ωL (V leads I by 90°); XC = 1/(ωC) (I leads V by 90°)
- LCR: Z = √[R² + (XL − XC)²]; tan φ = (XL − XC)/R
- Resonance: XL = XC; f₀ = 1/(2π√LC); Z = R (min); I = max
- Power: P = VIcos φ; pure L or C → P = 0 (wattless)
- Transformer: Vs/Vp = Ns/Np; losses: copper, iron, hysteresis, flux leakage
Previous: Ch 6 - Electromagnetic Induction
Next: Ch 8 - Electromagnetic Waves
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AC, Peak & RMS Values
Alternating current reverses direction periodically, so we describe it by its peak and rms values.
AC meters read rms. Indian mains: V_rms = 220 V, V0 ≈ 311 V, f = 50 Hz.
- Average over a full cycle = 0; rms is the DC that gives the same I2R heating
- Half-cycle mean = 2i0/π ≈ 0.637 i0 (don’t mix with rms)
- Chain: peak → divide by √2 → rms; start power problems from rms
Resistor in AC
A resistor obeys Ohm’s law instant by instant, so it never falls out of step.
R is the same at every frequency; the only element that dissipates power.
- Voltage and current peak at the same instant
- Opposition stays R for all frequencies
- Power is dissipated only here, never in pure L or C
Inductor & Capacitor (Reactance)
L and C react to the change in AC, so their opposition depends on frequency.
CIVIL: in C, I leads V; in L, V leads I. Both lag/lead by 90°.
- Inductor: current lags V by 90°; X_L rises with f (X_L = 0 at DC)
- Capacitor: current leads V by 90°; X_C falls with f (blocks DC, X_C → ∞)
- Pure L and pure C consume zero average power
Series LCR & Impedance
Same current flows through R, L, C but their voltages differ in phase, so add them as phasors.
V_L and V_C are 180° apart, so their phasors subtract — never add rms voltages arithmetically.
- V = √(V_R2 + (V_L − V_C)2); combine as vectors, not numbers
- Impedance Z is the AC version of resistance (in ohms)
- V_L or V_C can exceed the source voltage — that is normal
Phase in a Series LCR Circuit
The phase angle φ tells you whether the circuit behaves inductively or capacitively.
Keep the sign of (X_L − X_C) to judge inductive vs capacitive.
- X_L > X_C → inductive, voltage leads current
- X_C > X_L → capacitive, current leads voltage
- X_L = X_C → purely resistive (φ = 0), this is resonance
Resonance in Series LCR
When X_L = X_C the reactances cancel and the circuit draws maximum current.
At resonance Z = R (minimum, not zero); ω0 depends only on L and C, not R.
- Impedance minimum (Z = R), current maximum (I = V/R)
- Power factor = 1; circuit acts purely resistive
- Called an acceptor circuit — used to tune a radio
Quality Factor (Q)
Q measures how sharp and selective the resonance peak is.
Bandwidth Δf = f0/Q; high Q means a narrow band.
- High Q → tall, narrow peak → good selectivity
- Small R raises Q (R is in the denominator)
- High Q and high bandwidth are inverses, not the same
Power & Power Factor
AC power depends on the phase between voltage and current, captured by the power factor cos φ.
Use rms values, never peak. Power is dissipated only in R.
- Apparent power = V_rms I_rms (VA); true power = V_rms I_rms cos φ (W)
- Pure R: cos φ = 1 (max); pure L/C: cos φ = 0 → wattless current
- At resonance cos φ = 1, so power is maximum
Transformer & LC Oscillations
Both run on changing magnetic flux: a transformer reshapes AC voltage, an LC circuit oscillates on its own.
Transformer works only for AC (needs changing flux); ideal: V_p I_p = V_s I_s.
- Step-up: N_s > N_p (V up, I down); step-down: N_s < N_p (V down, I up)
- Real losses: copper (I2R), eddy currents (laminated core), hysteresis, leakage
- LC: energy swaps between capacitor’s electric field and inductor’s magnetic field (like SHM)
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Related Chapters in Class 12 Physics
- Electromagnetic Induction Class 12 Notes
- Moving Charges and Magnetism Class 12 Notes
- Electromagnetic Waves Class 12 Notes
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Frequently Asked Questions
The rms (root-mean-square) value is the steady DC current that would produce the same heating (I squared R) effect as the AC. We use it because the average of a sinusoidal AC over a full cycle is zero, and for a sinusoid I_rms = i0 divided by root 2, about 0.707 times the peak value.
Impedance is the total opposition to AC and equals Z = square root of [R squared plus (X_L minus X_C) squared], where X_L = 2 pi f L and X_C = 1 divided by (2 pi f C). The current then follows V_rms = I_rms times Z.
Resonance occurs when the inductive and capacitive reactances are equal (X_L = X_C), so they cancel and impedance becomes minimum (Z = R) while current is maximum. The resonant frequency is f0 = 1 divided by (2 pi root LC), and the circuit is called an acceptor circuit because it accepts maximum current at this frequency.
Yes, Alternating Current is part of the NEET Physics syllabus from Class 12 Electromagnetic Induction and AC, and it is largely numerical and high-yield. Questions commonly come from rms values, reactance, impedance, resonance and power factor, so it usually contributes a few marks each year.
Reactance is the opposition of a single inductor (X_L = omega L) or capacitor (X_C = 1 divided by omega C) and depends on frequency, while impedance Z is the combined total opposition of R, L and C together in the circuit. Reactance involves only L or C, whereas impedance also includes resistance and is found by phasor (vector) addition.