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Class 12 Physics Notes

Alternating Current Class 12 Physics Notes

Complete, exam-ready notes on alternating current: AC voltage and current, RMS and average values, phasors, LCR series circuits, impedance and reactance, resonance, power and power factor, and LC oscillations — written for CBSE boards, JEE and NEET revision.

Class12SubjectPhysicsCoversCBSE · JEE · NEET

Written byDeep Narayan· Science & Mathematics EducatorReviewed byPushpanjali

What is an alternating current in one line?

An alternating current changes direction periodically, usually sinusoidally: i = I₀ sin ωt, where I₀ is the peak value and the effective (RMS) value is I₀/√2 for domestic AC.

RMS and Average Values

RMS value

Irms=I02,Vrms=V02I_{\text{rms}} = \frac{I_0}{\sqrt{2}},\quad V_{\text{rms}} = \frac{V_0}{\sqrt{2}}

The RMS (root-mean-square) value is the DC equivalent that produces the same heating. Domestic Indian supply: 220 V220\,\text{V} RMS with frequency 50 Hz50\,\text{Hz}.

  • Average value over a full cycle is zero for a pure sine wave.
  • Peak value:
  • V0=2 VrmsV_0 = \sqrt{2}\,V_{\text{rms}}
  • .
  • Angular frequency:
  • ω=2πf\omega = 2\pi f
  • .
Irms=I02≈0.707 I0I_{\text{rms}} = \frac{I_0}{\sqrt{2}} \approx 0.707\,I_0
RMS relation

Reactance and Impedance

Impedance

Z=R2+(XL−XC)2Z = \sqrt{R^2 + (X_L - X_C)^2}

Impedance of a series LCR circuit resists AC. Inductive reactance XL=ωLX_L = \omega L, capacitive reactance XC=1ωCX_C = \frac{1}{\omega C}.

  • In a pure resistor, voltage and current are in phase.
  • In a pure inductor, current lags voltage by 90°.
  • In a pure capacitor, current leads voltage by 90°.
Z=R2+(XL−XC)2,XL=ωL,XC=1ωCZ = \sqrt{R^2 + (X_L - X_C)^2},\quad X_L = \omega L,\quad X_C = \frac{1}{\omega C}
Impedance and reactance

Resonance

Resonance condition

XL=XC⇒ω0=1LCX_L = X_C \Rightarrow \omega_0 = \frac{1}{\sqrt{LC}}

At resonance in a series LCR circuit, reactances cancel, impedance is minimum (Z = R), and current is maximum. The resonant frequency is f0=12πLCf_0 = \frac{1}{2\pi\sqrt{LC}}.

  • Quality factor:
  • Q=ω0LRQ = \frac{\omega_0 L}{R}
  • — sharpness of resonance.
  • At resonance the inductor and capacitor voltages can exceed the source voltage (Q times).
  • Used in radio tuning — matching the resonant frequency to the desired station.
ω0=1LC,Q=ω0LR\omega_0 = \frac{1}{\sqrt{LC}},\quad Q = \frac{\omega_0 L}{R}
Resonance and quality factor

Power and Power Factor

Power in AC

P=VrmsIrmscos⁡ϕP = V_{\text{rms}}I_{\text{rms}}\cos\phi

The average power depends on the power factor cosφ, where φ is the phase angle between voltage and current: cos⁡ϕ=RZ\cos\phi = \frac{R}{Z}.

No power in pure reactive elements

In a purely inductive or capacitive circuit the power factor is zero and the average power is zero — energy sloshes back and forth but no net work is done.

LC Oscillations

In an LC circuit, energy alternately stores in the capacitor (electric) and inductor (magnetic), oscillating at the natural frequency ω=1LC\omega = \frac{1}{\sqrt{LC}}. In an ideal circuit with no resistance, the oscillations persist.

Conservation analogy

LC oscillation is analogous to a mass-spring system: charge q ↔ displacement, current i ↔ velocity, capacitor energy ↔ potential energy, inductor energy ↔ kinetic energy.

Solved Examples

Example: A series LCR circuit has R=6 ΩR = 6\,\Omega, XL=10 ΩX_L = 10\,\Omega, XC=2 ΩX_C = 2\,\Omega. Find the impedance.

Solution: Z=62+(10−2)2=36+64=100=10 ΩZ = \sqrt{6^2 + (10-2)^2} = \sqrt{36+64} = \sqrt{100} = 10\,\Omega.

Revision

Key formulas at a glance

Memorise these before attempting numericals — most exam questions hinge on one of them.

RMS value

Irms=I02I_{\text{rms}} = \frac{I_0}{\sqrt{2}}

Impedance

Z=R2+(XL−XC)2Z = \sqrt{R^2 + (X_L - X_C)^2}

Inductive reactance

XL=ωLX_L = \omega L

Capacitive reactance

XC=1ωCX_C = \frac{1}{\omega C}

Resonant frequency

ω0=1LC\omega_0 = \frac{1}{\sqrt{LC}}

AC power

P=VrmsIrmscos⁡ϕP = V_{\text{rms}}I_{\text{rms}}\cos\phi

Exam tips

How this chapter is asked

Where this topic appears in CBSE, JEE Main and NEET papers.

  • RMS = peak/√2.
  • Impedance of pure LCR: Z = √(R² + (X_L − X_C)²).
  • Resonance when ω₀ = 1/√LC.
  • AC power = V_rms I_rms cosφ.
  • Pure L/C has zero average power (cosφ = 0).

FAQ

Common questions

What is RMS value and why is it used?

The RMS value is the DC equivalent producing the same heating as the AC, I_rms = I₀/√2. It lets us use DC power formulas for AC.

What is resonance in an LCR circuit?

When inductive and capacitive reactances cancel (X_L = X_C at ω₀ = 1/√LC), impedance is minimum, current is maximum, and the circuit is most sensitive to that frequency.

What is the power factor?

The cosine of the phase angle between voltage and current, cosφ = R/Z. It measures how much of the apparent power is real power.

Why is no power consumed by a pure inductor?

The inductor stores energy and returns it to the source — average power over a cycle is zero because current lags voltage by 90° (cosφ = 0).

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Related notes

All Class 12 NotesClass 12 Electromagnetic Induction NotesClass 12 Current Electricity NotesPhysics Tutor in Mohali

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