Chapter 7 - Alternating Current

The current supplied to homes does not flow continuously in one direction. It reverses direction periodically.

Alternating Current Class 12 studies alternating voltage and current, their behaviour in resistors, inductors and capacitors, LCR circuits, resonance, electrical power, AC generators and transformers.

Alternating current and voltage

An alternating current changes both magnitude and direction periodically.

A sinusoidal alternating current can be described using:

• Peak value

• Angular frequency

• Frequency

• Time period

• Phase

The instantaneous current varies throughout the cycle.

RMS values

Because alternating current changes continuously, its simple average over a complete cycle is zero.

The root mean square value gives the equivalent direct current that would produce the same heating effect in a resistor.

Household AC ratings generally refer to RMS values, not peak values.

AC through a resistor

In a purely resistive circuit:

• Current and voltage are in phase

• Electrical energy is continuously dissipated as heat

• Opposition is ordinary resistance

The current reaches its maximum and minimum at the same times as voltage.

AC through an inductor

An inductor opposes changes in current through self-induction.

In a purely inductive circuit, current lags voltage by a quarter cycle.

The opposition offered by an inductor is called inductive reactance. It increases with frequency.

AC through a capacitor

A capacitor repeatedly charges and discharges in an AC circuit.

In a purely capacitive circuit, current leads voltage by a quarter cycle.

Capacitive reactance decreases as frequency increases.

Series LCR circuit

A series LCR circuit contains resistance, inductance and capacitance.

Its total opposition to AC is called impedance.

Students use phasor diagrams to combine:

• Resistive voltage

• Inductive voltage

• Capacitive voltage

Because these voltages are not all in phase, they cannot always be added arithmetically.

Resonance

Resonance occurs when inductive reactance equals capacitive reactance.

At resonance in a series LCR circuit:

• Net reactance is zero

• Impedance is minimum

• Current is maximum

• Voltage and current are in phase

• Power factor becomes maximum

Resonance is used in tuning and frequency-selection systems.

Power in AC circuits

Average power depends on:

• RMS voltage

• RMS current

• Power factor

The power factor indicates the fraction of apparent electrical power converted into average useful power.

In a purely inductive or capacitive circuit, average power over a complete cycle is zero. Such current is called wattless current under the ideal model.

AC generator

An AC generator converts mechanical energy into electrical energy using electromagnetic induction.

A rotating coil experiences changing magnetic flux, producing alternating EMF.

Students study the principle and basic operation of an AC generator.

Transformer

A transformer changes alternating voltage using mutual induction.

A step-up transformer increases voltage and decreases current ideally. A step-down transformer decreases voltage and increases current.

Transformers require changing current. They do not operate normally with steady DC.

High-voltage transmission reduces current for the same power and therefore reduces resistive energy loss in transmission lines.

Common student difficulties

Students frequently:

• Confuse peak and RMS values

• Forget phase relationships

• Add AC voltages arithmetically instead of using phasors

• Mix resistance, reactance and impedance

• Use the resonance condition incorrectly

• Assume an ideal inductor consumes average power

• Think a transformer can operate on steady DC

• Ignore power factor

Learning with Teachoo

Teachoo provides:

• Waveform and phasor diagrams

• RMS-value derivations

• LCR-circuit numericals

• Resonance questions

• AC-power problems

• Generator and transformer explanations

• NCERT solutions

• MCQs and case-based questions

Frequently Asked Questions

Why is the average AC current over a complete cycle zero?

Positive and negative halves cancel algebraically.

Why do we use RMS current?

RMS current gives the equivalent DC value that produces the same heating effect in a resistor.

What happens at resonance in a series LCR circuit?

Inductive and capacitive reactances cancel, impedance becomes minimum and current becomes maximum.

Does a pure inductor consume average power?

Ideally, no. It stores energy temporarily and returns it during the cycle.

Can a transformer work with DC?

Not with steady DC because mutual induction requires changing magnetic flux.

Why is electricity transmitted at high voltage?

For the same power, higher voltage allows lower current, reducing resistive power loss.