Alternating Current

part 1

AC Basics and Resistive Circuits

• AC voltage and current — peak and RMS values
• AC through a resistor
• AC through an inductor
• AC through a capacitor

part 2

LCR Circuits

• AC through series LCR circuit
• Phasor diagram analysis
• Resonance in LCR circuit
• Sharpness of resonance (Q factor)
• Power factor and wattless current

part 3

Power and Transformers

• Power in AC circuits
• LC oscillations
• Transformer — principle, working, efficiency
• Energy losses in transformers

Instantaneous values & RMS

$e = E_0\sin\omega t$; $E_{rms} = \frac{E_0}{\sqrt{2}}$; $I_{rms} = \frac{I_0}{\sqrt{2}}$

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Inductive reactance

$X_L = \omega L = 2\pi f L$ (unit: Ω)

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Capacitive reactance

$X_C = \frac{1}{\omega C} = \frac{1}{2\pi f C}$ (unit: Ω)

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Impedance of series LCR

$Z = \sqrt{R^2 + (X_L - X_C)^2}$

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Phase angle φ

$\tan\phi = \frac{X_L - X_C}{R}$

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Resonance condition

$X_L = X_C$ → $\omega_0 = \frac{1}{\sqrt{LC}}$

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Resonant frequency

$f_0 = \frac{1}{2\pi\sqrt{LC}}$

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Average power in AC circuit

$P = E_{rms} \cdot I_{rms} \cdot \cos\phi = I^2_{rms} \cdot R$

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Transformer turns ratio

$\frac{V_2}{V_1} = \frac{N_2}{N_1} = \frac{I_1}{I_2}$

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Power factor

$\cos\phi = \frac{R}{Z}$

★ frequently asked

For a series LCR circuit, derive the condition for resonance and the expression for the resonant frequency. Define quality factor (Q) and explain its significance in a resonant circuit.

Define power factor of an AC circuit. What is the average power dissipated in an ideal (pure) inductor connected to an AC source? Give reason.

Draw a phasor diagram for a series LCR circuit with AC source. Derive an expression for the impedance and current in the circuit. Under what condition does resonance occur?

An AC voltage V = V₀ sin ωt is applied across a pure inductor of inductance L. Derive the expression for the current, and show that the current lags the voltage by π/2. Define inductive reactance.

State the principle of a transformer. A step-up transformer has 100 turns in primary and 500 turns in secondary. If the primary voltage is 220V and the primary current is 5A, find the secondary voltage and current (assume 100% efficiency).

How does the capacitive reactance of a capacitor change when the frequency of the AC source is doubled?

The peak voltage of an AC source is 300V. What is its RMS voltage?

What is meant by a wattless current? In an AC circuit, under what condition is the power dissipated (i) maximum and (ii) zero?

State any two sources of energy loss in a transformer and mention how each can be minimised.

How many marks is Alternating Current worth in the Class 12 board exam?

Around 2 marks of the 70-mark CBSE Physics theory paper, based on the official unit-wise weightage. LCR resonance — often a short 2-mark concept question.

Is Alternating Current easy or hard?

It's rated hard — one of the tougher chapters in Class 12 Physics. Most students need about 4 hours to cover it well.

What are the important topics in Alternating Current?

The chapter covers 12 NCERT topics in 3 areas: AC Basics and Resistive Circuits; LCR Circuits; Power and Transformers.

What questions come from Alternating Current in board exams?

Between 2018–2024, CBSE board papers asked questions from this chapter on Resonance in LCR, Power in AC, LCR Circuit, AC through Inductor — 1- to 5-mark questions.