Physics notesElectromagnetismAC & EM Waves
Independent topic page
Reduce series LCR to Z and φ with phasors, then read I₀, V drops and power; EM waves need c=1/√(μ₀ε₀), E–B link and spectrum order radio→γ.
01. Series LCR: X_L=ωL, X_C=1/(ωC), Z=√[R²+(X_L−X_C)²], tanφ=(X_L−X_C)/R. I₀=V₀/Z.
02. Resonance ω₀=1/√(LC): X_L=X_C, Z=R, current max, φ=0. Sharpness related to Q=ω₀L/R.
03. Average power P̄ = V_rms I_rms cosφ = I_rms² R (only R dissipates).
04. EM waves: transverse, E⊥B⊥k, speed c in vacuum; intensity ideas and spectrum radio → microwave → IR → visible → UV → X → γ with elementary uses.
05. AC series LCR: impedances add as X_L−X_C on the imaginary axis with R. Resonance ω₀=1/√(LC); Z min =R; current max. Phase: current lags voltage in inductive nets.
06. Power ⟨P⟩=V_rms I_rms cosφ with cosφ=R/Z. rms = peak/√2 for sinusoids. Transformers and phasors are geometry in the complex plane—draw the phasor before formulas.
07. EM waves in vacuum: c=1/√(ε₀μ₀), E and B in phase, E/B=c, energy flux S=E×H. Displacement current closes Ampère when conduction current is missing between capacitor plates.
Official · 2026
Official syllabus points for AC Circuits & EM Waves only — not the full Electromagnetism portion map. Portion hub: Electromagnetism · Magnetism/EMI/AC analysis.
No topic-specific exclusions flagged — finish the unit points below for AC & EM Waves.
Source: https://jeeadv.ac.in/documents/jee-advanced-2026-syllabus.pdf
Exam focusAC LCR circuits, resonance, power factor, and EM-wave basics.
Syllabus points
Do / check
2020–2026 paper weight
Topic match inside parent portion Magnetism/EMI/AC (9.8% of Physics tags). Stats below are portion backdrop; matched subtopics show where AC Circuits & EM Waves sits.
Portion-wide type/difficulty mix lives on the Magnetism/EMI/AC analysis — not repeated here so this page stays on AC & EM Waves.
01. Magnetism/EMI/AC accounts for ~9.8% of tagged physics questions (2020–2026).
02. Dominant subtopics: EMI/AC (12), Magnetism (11).
Cross-topic stems
Advanced rarely asks a chapter in isolation. These are tagged multi-idea Physics stems that touch AC Circuits & EM Waves — practise the knowledge bridge, not only the single-chapter drill.
Step 1: read the coupling M = L/2 and series inductance to form L_eff. Step 2: replace the network by one equivalent L_eff (here 3L/4). Step 3: apply ω₀ = 1/√(L_eff C) to get 2/√(3LC).
Students remember ω=1/√(LC) but forget to rebuild L_eff from mutual terms.
For every coupled-inductor problem, compute L_eff first, then resonate.
Step 1: write induced emf from flux change. Step 2: place that source in the AC network (reactances). Step 3: test each option for amplitude, phase and limiting behaviour separately.
MC options mix Faraday facts with circuit phasors.
Separate ‘induction law’ checks from ‘impedance algebra’ checks on paper.
Step 1: isolate the electromagnetic law needed (flux/induced emf/impedance). Step 2: compute the asked scalar. Step 3: consciously leave rotation kinematics behind so constants are not mixed.
Topic island inside a Mechanics-heavy NUM sea.
Underline the chapter keywords in each NUM stem before writing equations.
Why methods matter
One phasor impedance triangle yields current amplitude, phase and average power.
Makes V_L+V_C+V_R ≠ V_source as a feature, not a bug.
Do thisDraw V_R along I; V_L lead I by 90°; V_C lag by 90°; net reactive V_L−V_C.
Makes V_L+V_C+V_R ≠ V_source as a feature, not a bug.
At resonance V_L=V_C so they cancel in the phasor sum; both can still be ≫ V_R.
Kills wrong Z(ω) sketches quickly.
Do thisIf ω unknown, test ω→0 (C open-ish behaviour) and ω→∞ (L open-ish) for qualitative MC.
Kills wrong Z(ω) sketches quickly.
Series LCR: Z→∞ as ω→0 or ω→∞; minimum at ω₀.
Reactive elements store and return energy over a cycle.
Do thisCompute I_rms then P̄=I_rms² R; ignore L and C for average power.
Reactive elements store and return energy over a cycle.
cosφ = R/Z; P̄ = V_rms I_rms (R/Z).
Elementary-use stems are matching, not calculation.
Do thisMemorise order radio→γ and one use each; match wavelength/frequency trends inversely.
Elementary-use stems are matching, not calculation.
UV: photoelectric/sterilisation; X: medical imaging; γ: nuclear; radio: communication.
Processed examples
Read the impact line first. Then notice which family/model was chosen. The solution is written the way your rough sheet should look in the hall.
In a series LCR, R=30 Ω, X_L=50 Ω, X_C=10 Ω. Find Z.
This stem rewards early recognition of the series lcr phasors model.
Model chosenZ=√[R²+(X_L−X_C)²].
Answer50 Ω
Takeaway: Net reactance is X_L−X_C.
V_rms=200 V, I_rms=2 A, cosφ=0.5. Find average power.
This stem rewards early recognition of the power in ac circuits model.
Model chosenP=V I cosφ.
Answer200 W
Takeaway: Average power uses the power factor.
A series LCR circuit has R=30 Ω, L=0.2 H, C=50 μF and V=200 V (rms) at ω=100 rad/s? Actually drive frequency f such that ω=100? Use ω=100 rad s⁻¹? 1/√(LC)=1/√(0.2·50×10⁻⁶)=10³/√10. Take ω=500 rad/s. Find current amplitude and phase of current relative to voltage.
This Advanced-level variation couples hidden constraints with the series lcr phasors model.
Model chosenCompute X_L, X_C, then Z and φ.
AnswerI₀≈4.22 A; current lags by tan⁻¹2
Takeaway: Phasor Z decides both amplitude and lead/lag in one step.
Reusable models
Advanced stems cluster. Name the family in 10–15s, write the fast model, then run the same path. Do not invent a new plan each time.
Looks likeZ, phase, I₀, resonance
Fast modelZ=√[R²+(X_L−X_C)²]; tanφ=(X_L−X_C)/R.
Recognition fixes the model before arithmetic begins.
Do not start blind expansion or casework before identifying the governing model.
Looks likeP=V_rms I_rms cosφ; wattless current
Fast modelAverage power uses cosφ; ideal L/C average to zero alone.
Recognition fixes the model before arithmetic begins.
Do not start blind expansion or casework before identifying the governing model.
Looks likeLead/lag, high-pass/low-pass behavior
Fast modelCapacitor: current leads V; inductor: current lags.
Recognition fixes the model before arithmetic begins.
Do not start blind expansion or casework before identifying the governing model.
Looks likec=1/√(μ₀ε₀); E/B=c; spectrum order
Fast modelUse relation set; do not invent medium formulas.
Recognition fixes the model before arithmetic begins.
Do not start blind expansion or casework before identifying the governing model.
Hall timing
Underline charges, geometry, symmetry, source type and the exact ask (E, V, flux, I, B, Φ, energy). Reject any formula whose assumptions are already broken.
Write the governing law symbolically before numbers: Coulomb/Gauss, Kirchhoff, Biot–Savart/Ampere, Faraday/Lenz, or phasor impedance. Fix sign convention and reference once.
Compute with ratios and conserved quantities first. Carry direction, SI units and powers of ten on the rough sheet instead of repairing them at the end.
Check dimensions, limiting cases (κ→1, r→∞, ω→0/∞) and physical sense. For multi-correct, test every option independently.
After the model is locked
X_L=ωL; X_C=1/(ωC)
Sinusoidal steady state
Z=√[R²+(X_L−X_C)²]; I₀=V₀/Z
Series LCR
tanφ=(X_L−X_C)/R (φ of V ahead of I)
Lag/lead
ω₀=1/√(LC); Z_min=R
Series resonance
V_rms=V₀/√2; P̄=V_rms I_rms cosφ=I_rms² R
Average AC power
c=1/√(μ₀ε₀)=E₀/B₀
Vacuum plane wave
I ∼ E₀ B₀/(2μ₀) = ½ c ε₀ E₀²
Intensity order (plane wave)
Make it automatic