Alternating Current and Electromagnetic Waves: Concepts, Formulas and Tips for NEET by Physics Wallah

Many NEET students find alternating current and electromagnetic waves hard because the chapter mixes many formulas, phase rules and definitions. It is easy to confuse peak and RMS values, or to forget which of the inductor and capacitor leads the current. A small slip in any of these can cost marks in the exam.

The given details below follow a clear order: DC and AC, how they are measured, RMS values, circuits with R, L and C, resonance, transformers, and then electromagnetic waves. Each part uses short points and memory tips for quick revision. PW’s online Physics classes can also help you practise the same chapter with notes and tests.

What Are Direct Current and Alternating Current?

Direct current (DC) flows in one direction only. Alternating current (AC) changes its direction again and again. Knowing this difference first makes the rest of the chapter easier to follow.

Direct current (DC)

• Unidirectional: Current always flows in one direction. A DC source gives a direct voltage.

• Constant or variable size: The direction is fixed, but the size can be constant, as from a battery, or can vary, as in pulsating DC from a rectifier without filtering.

• Waveforms: Current vs. time graphs can show constant positive DC, constant negative DC or varying positive DC.

Alternating current (AC)

• Bidirectional: Current flows in both positive and negative directions.

• Periodic: The waveform repeats after a fixed time called the period (T).

• Symmetric: The positive half-cycle matches the negative half-cycle, so the average value over a full cycle is zero.

• Waveforms: Sinusoidal, square and triangular AC are examples of pure AC.

AC vs DC: Advantages and Disadvantages

Both types of current have strong and weak points. The table below puts them side by side so you can compare them quickly before an exam.

How Does Current Flow in a Wire?

DC and AC spread through a wire in different ways. This difference explains why power lines are built from stranded wires.

• DC: Current flows evenly through the whole cross-section of the wire. A constant current makes a constant magnetic field, so there is no induced back EMF to oppose the flow in the bulk of the conductor.

• AC (skin effect): Current flows mainly along the surface. A changing current makes a changing magnetic field, which induces a back EMF. This back EMF pushes the current towards the surface and opposes flow in the inner part.

Because of the skin effect, AC transmission uses many stranded wires instead of one thick wire. This increases the effective surface area.

Memory tip: DC flows through the Deep Centre (cross-section). AC flows along the All Circumference (surface).

How Are AC and DC Measured?

Two instruments are common in this chapter, and they work on different principles.

• Moving coil galvanometer (MCG): It works on the torque on a current-carrying coil in a magnetic field. It measures only DC. The coil has inertia and cannot follow the fast reversals of AC, so it shows no deflection.

• Hot wire ammeter: It works on the heating effect of current. Heat is proportional to I²Rt, and it makes the wire expand. It measures both AC and DC. Since heat depends on I², its scale is non-linear.

Memory tip: MCG measures DC only. The hot wire ammeter measures both AC and DC.

Average and RMS Value of Alternating Current

Average and RMS values are asked often, so learn both clearly. The average value is the mean over a time interval, while the RMS value is the effective value that gives the same heating effect as a DC current.

Average Current

• Discrete values: I_avg = (I₁ + I₂ + ... + Iₙ) / n

• Continuous current I(t) from t₁ to t₂: I_avg = (∫ I(t) dt from t₁ to t₂) / (t₂ − t₁)

For sinusoidal AC, I = I₀ sin(ωt). The average over a full cycle (0 to T) is zero because of symmetry. Over a half cycle (0 to T/2), it is 2I₀/π.

Memory tip: for any pure AC waveform, the average value over a full cycle is zero.

RMS Value

Memory tip: read RMS backwards: Square, Mean, Root.

1. Square: Find I²(t).

2. Mean: Find the average of I²(t) over the interval: ⟨I²⟩ = (∫ I²(t) dt) / (t₂ − t₁).

3. Root: I_rms = √⟨I²⟩.

For sinusoidal AC, I_rms = I₀ / √2 and V_rms = V₀ / √2.

The table below lists the average and RMS values for three common waveforms. Notice that the full-cycle average is zero in every case.

Mixture of AC and DC

For a current I = I₁ + I₂ sin(ωt), where I₁ is the DC part and I₂ is the AC peak, the RMS value is I_rms = √(I₁² + I₂²/2). In the same way, I_RMS = √(I_DC² + (I_peak_AC / √2)²).

Reading a Sinusoidal Equation

For I = I₀ sin(ωt + φ):

• I₀: Peak current

• ω: Angular frequency

• φ: Initial phase

From these you can find frequency (f = ω/2π), time period (T = 1/f, or T = 2π/ω), peak-to-peak current (2I₀), RMS current (I₀/√2) and the instantaneous current. Some useful times in one cycle:

• Zero to peak value: T/4

• Zero to RMS value: T/8

• Maximum to RMS value: T/8

AC Circuits with Resistor, Capacitor and Inductor

The three basic parts behave differently when an AC source is connected. The main differences are in the phase between voltage and current and in the power used.

AC Source Across a Pure Resistor

• Current: I = (E_peak / R) sin(ωt), so I_peak = E_peak / R.

• Current and voltage are in the same phase (0° difference).

• Impedance: Z = R.

• Average power loss: P_avg = V_RMS × I_RMS.

Memory tip: when confused, assume that ammeters and voltmeters in AC circuits read RMS values.

AC Source Across a Pure Capacitor

• Capacitive reactance: X_C = 1/(ωC) = 1/(2πfC). It is inversely proportional to C and f.

• Peak current: I_peak = E_peak / X_C.

• Current leads voltage by 90° (π/2).

• Average power loss is zero, so it is a wattless circuit.

• Inserting a dielectric increases C, decreases X_C and increases the current.

AC Source Across a Pure Inductor

• Inductive reactance: X_L = ωL = 2πfL. It is directly proportional to L and f.

• Peak current: I_peak = E_peak / X_L.

• Voltage leads current by 90° (π/2).

• Average power loss is zero, so it is a wattless circuit.

• Inserting an iron core increases L, increases X_L and decreases the current.

The table below sums up the phase rules. It also shows the memory tip “ELI the ICE man”, which helps you recall which quantity leads.

Series RL, RC, LC and LCR Circuits

In series AC circuits, RMS or peak voltages do not simply add up, because the voltages have phase differences.

• Series RL: Z = √(R² + X_L²). Phase angle φ = tan⁻¹(X_L / R), and voltage leads current.

• Series RC: Z = √(R² + X_C²). Phase angle φ = tan⁻¹(X_C / R), and current leads voltage.

• Series LC: Z = |X_L − X_C|. Net voltage V_net = |V_L − V_C|. The phase difference is 90°, except at resonance.

Average Power in AC Circuits

P_avg = V_RMS × I_RMS × cos φ, where cos φ is the power factor.

• Wattful (active) current: I_RMS cos φ, which causes power loss.

• Wattless (reactive) current: I_RMS sin φ, which gives no average power. Purely inductive or capacitive circuits are wattless.

• Maximum power is lost only in a purely resistive circuit.

Series LCR Circuit

• Net voltage: V_net = √(V_R² + (V_L − V_C)²)

• Impedance: Z = √(R² + (X_L − X_C)²)

• Power factor: cos φ = R / Z

• Peak current: I_peak = V_peak / Z

Resonance in a Series LCR Circuit

Resonance occurs when X_L = X_C. The resonant angular frequency is ω₀ = 1/√(LC), and the resonant frequency is f₀ = 1/(2π√(LC)). At resonance:

• V_L = V_C, so the two voltages cancel.

• Impedance is minimum: Z = R.

• Current is maximum: I = V/R.

• Phase difference is 0°, so the circuit is purely resistive.

• Power factor is 1, which is the maximum, and average power loss is also maximum.

The table below shows how the circuit behaves as the frequency changes around ω₀. It is a quick way to decide if the circuit acts as a capacitor, a resistor or an inductor.

Quality Factor and Bandwidth

• Bandwidth (Δω): The range of frequencies between the half-power points. Δω = R/L.

• Quality factor (Q): It measures how sharp the resonance is. A higher Q means sharper resonance and better selectivity. Q = ω₀/Δω = (1/R) × √(L/C). Q has no units and no dimensions.

Inductor and Capacitor in DC and AC

The table below compares how an inductor and a capacitor act with a DC source and an AC source. Remember that DC means frequency f = 0.

How Do Transformers Work?

A transformer works on the principle of mutual induction and works only on AC. An ideal transformer has 100% efficiency.

• Voltage ratio: V_output / V_input = N_s / N_p. Voltage is directly proportional to the number of turns.

• Power: For an ideal transformer, P_p = P_s.

• Current ratio: I_s / I_p = V_p / V_s = N_p / N_s. Current is inversely proportional to the number of turns.

• Efficiency: η = P_output / P_input = (V_s × I_s) / (V_p × I_p).

A real transformer loses energy through flux leakage, winding resistance (I²R loss), eddy currents and hysteresis loss.

The table below compares the two types of transformers. The key point is that the current moves opposite to the voltage.

Electromagnetic Waves

Electromagnetic (EM) waves began with a gap in the old laws of magnetism. Maxwell closed this gap with the idea of displacement current, and this led to the four equations that join electricity and magnetism.

Displacement Current

Maxwell introduced displacement current (I_D) to fix an inconsistency about the magnetic field between capacitor plates. A changing electric field creates the displacement current, which completes the circuit.

• I_D = ε₀ (dΦ_E/dt)

• For a capacitor, I_D = C (dV/dt)

• During charging, the drift current in the wires equals the displacement current between the plates.

• Displacement current flows evenly across the plate area, unlike the drift current, which is localised.

Maxwell’s Equations

The table below lists the four equations and what each one means. Learn the meaning along with the form, because questions often ask for the meaning.

Properties of EM Waves

• Transverse: The E and B fields are perpendicular to the direction of travel.

• Non-mechanical: They need no medium and can travel through a vacuum.

• Field oscillations: E and B oscillate in phase and are perpendicular to each other. The direction of travel is v̂ = Ê × B̂.

• Speed: v = 1/√(με). In free space, c = 1/√(μ₀ε₀). In a medium, v = c/√(μ_r ε_r).

• Ratio of fields: c = E/B.

• Transport: They carry energy, momentum and information, but not charge. Electric and magnetic fields do not deflect them.

Energy, Poynting Vector and Intensity

• Energy is shared equally between the electric and magnetic fields.

• Instantaneous total energy density: u = ε₀E² = B²/μ₀.

• Average total energy density: u_avg = ½ ε₀E₀² = ½ B₀²/μ₀.

• Poynting vector: S = (E × B)/μ₀. It shows the energy flow per unit area per unit time.

• Intensity: The average power per unit area, equal to the average size of the Poynting vector. I = u_avg × v.

Sources of EM Waves

• Accelerating charges

• LC oscillations

• Transition of electrons (visible and UV)

• Retardation of electrons (X-rays)

• De-excitation of nuclei (gamma rays)

Electromagnetic Spectrum

The spectrum orders EM waves by wavelength, frequency and energy. From shortest to longest wavelength, the order is:

Gamma rays → X-rays → Ultraviolet → Visible light → Infrared → Microwaves → Radio waves

From gamma rays to radio waves, the wavelength increases, while the frequency and the energy decrease.

Exam Tips and Common Mistakes to Avoid

• Full-cycle average: For any pure AC waveform, it is zero. Use the half-cycle value when a question asks for it.

• Meter readings: Assume ammeters and voltmeters in AC circuits show RMS values.

• Phase rule: Use ELI the ICE man to avoid mixing up the inductor and the capacitor.

• Series voltages: Do not add voltages in series circuits directly. Use the phase-based formulas.

• Instruments: An MCG cannot measure AC, but a hot wire ammeter can.

• Resonance: Z is minimum, current is maximum, and the power factor is 1.

• EM waves: They do not carry charge and are not deflected by electric or magnetic fields.

Once you link each circuit to its phase rule, formula and memory tip, alternating current and electromagnetic waves become much easier to revise. For regular practice with live classes and tests, you can explore PW NEET online coaching.

Related Resources

• NEET Physics syllabus

• Class 12 Physics notes

• Electromagnetic Induction

• NEET Physics important chapters

• Alternating Current previous year questions

• NEET previous year question papers