Alternating Current

Alternating Current Class 12th Topics (NCERT Syllabus)

1. Introduction

So far, we have studied direct current (dc), which does not change direction with time. However, in real life, most electrical energy is supplied as alternating current (ac), where voltage and current vary with time like a sine wave. AC is preferred because it can be easily transformed to higher or lower voltages, making long-distance transmission more efficient. Many devices, from household appliances to radios, make use of the unique properties of ac circuits.

2. AC Voltage Applied to a Resistor

When an alternating voltage $v(t)=V_0 \sin \omega t$ is applied across a pure resistor $R$, the current is given by

$
i(t)=\frac{V_0}{R} \sin \omega t=I_0 \sin \omega t
$

• AC Voltage Applied to a Resistor

3. Representation of AC Current and Voltage by Rotating Vectors – Phasors

In AC circuits, current and voltage change continuously with time. To represent these changing quantities more simply, we use phasors. A phasor is a rotating vector that shows both the magnitude and phase (angle) of a sinusoidal quantity. The length of the phasor represents the maximum value (amplitude), and its angular position represents the phase at a given instant. This method makes it easier to analyze AC circuits and understand the phase difference between current and voltage in different components like resistors, capacitors, and inductors.

• AC Circuit

4. AC Voltage Applied to an Inductor

When an AC voltage is applied to a pure inductor, the current does not stay in phase with the voltage. Instead, the current lags the voltage by $90^{\circ}$ ( $\pi / 2$ radians). The opposition offered by the inductor to the changing current is called inductive reactance (XL = $\boldsymbol{\omega L}$ ), where $\omega$ is the angular frequency and $L$ is the inductance. The RMS current is given by:

$
I=\frac{V}{X_L}=\frac{V}{\omega L}
$

Thus, in an AC circuit with a pure inductor, the voltage leads the current by $90^{\circ}$.

• AC Voltage Applied to an Inductor

5. AC Voltage Applied to a Capacitor

When an AC voltage is applied to a pure capacitor, the current leads the voltage by $90^{\circ}$ ( $\pi / 2$ radians). The opposition offered by the capacitor to the changing current is called capacitive reactance (XC = 1/ $\boldsymbol{\omega} \mathbf{C )}$, where $\boldsymbol{\omega}$ is the angular frequency and $\boldsymbol{C}$ is the capacitance. The RMS current is given by:

$
I=\frac{V}{X_C}=V \cdot \omega C
$

Thus, in a purely capacitive AC circuit, the current leads the voltage by $90^{\circ}$.

• AC Voltage Applied to a Capacitor

6. AC Voltage Applied to a Series LCR Circuit

When an AC voltage is applied to a series circuit containing a resistor (R), inductor (L), and capacitor (C), all three components share the same current but the voltage across each is different. The resistor's voltage is in phase with the current, the inductor's voltage leads the current by $90^{\circ}$, and the capacitor's voltage lags the current by $90^{\circ}$.

The total opposition to current is called impedance (Z):

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

where $X_L=\omega L$ is inductive reactance and $X_C=\frac{1}{\omega C}$ is capacitive reactance.
The current is given by:

$
I=\frac{V}{Z}
$

The phase difference between current and voltage depends on the values of $R, L$, and $C$. At resonance ( $X_L=X_C$ ), the impedance is minimum and current is maximum.

• AC Voltage Applied to a Series LCR Circuit
• LRC Circuit Phasor Diagram

7. Power in AC Circuit: The Power Factor

In an AC circuit, power depends on both voltage and current as well as the phase difference between them. The average power consumed is given by:

$
P=V I \cos \phi
$

Here, $V$ and $I$ are the RMS values of voltage and current, and $\phi$ is the phase difference.
The term $\cos \phi$ is called the power factor.

If $\cos \phi=1$, the circuit is purely resistive and power is maximum.

If $\cos \phi=0$, as in purely inductive or capacitive circuits, no average power is consumed.

• Power And Power Factor In AC Circuits
• Quality Factor In An AC Circuit
• Resonance In Series LCR Circuit

8. Transformers

A transformer is a device that changes (steps up or steps down) the alternating voltage without changing the frequency. It works on the principle of mutual induction.
A transformer consists of two coils, the primary coil and the secondary coil, wound on a soft iron core.
The voltage across the coils is related as:

$
\frac{V_s}{V_p}=\frac{N_s}{N_p}
$

where $V_s$ and $V_p$ are the secondary and primary voltages, and $N_s$ and $N_p$ are the number of turns.

• Transformers

Related Topics,

Exam-wise Weightage of Alternating Current

Approach to solve Alternating current questions

To solve $A C$ questions, first try to understand the current and voltage with the help of phasor diagrams (they show how current and voltage are related). Remember the formulas of current and voltage for a resistor, inductor, and capacitor. For a series LCR circuit, use Ohm's law in phasor form and calculate impedance (Z). Pay extra attention to resonance, where the inductor and capacitor effects cancel out $(X_L=X_C)$. In power questions, always use the power factor ( $\boldsymbol{\operatorname { c o s }} \boldsymbol{\phi}$ ) to find the average power. For board exams, focus more on derivations and graphs, while for JEE/NEET, practice numerical problems on resonance, transformers, and LCR circuits.

Alternating Current Real Life Example

• Home Supply – Fans, lights, TVs, and refrigerators work on AC from power stations.
• Transformers – AC can be increased or decreased for safe long-distance power transmission.
• Radio/TV Tuning – AC circuits help select the right frequency.
• Industries – Big machines run on AC motors.
• Medical Use – X-ray and MRI machines work using AC.

NCERT Notes Subject wise link:

• NCERT Notes for class 12 Physics.
• NCERT Notes for class 12 Chemistry.
• NCERT Notes for class 12 Mathematics.
• NCERT Notes for class 12 Biology.

Importance of alternating current for class 12

Physics contains the greatest chapters that will provide pupils with a solid foundation. The chapter on the alternating current will help students understand the fundamentals of electricity a bit better. Class 12 Chapter 7 Physics aid’s pupils in comprehending all definitions and topics related to alternating current. Alternating Current is a simple and high-scoring chapter in both the JEE Mains and JEE Advanced exams. This chapter focuses only on the behaviour of various types of AC circuits, including resistor, capacitor, and inductor circuits. It also discusses phasors, which is an important topic.

• NCERT solutions for class 12 physics chapter alternating current
• NCERT exemplar solutions for class 12 physics chapter alternating current
• NCERT notes for class 12 physics chapter alternating current

NCERT Solutions Subject wise link:

• NCERT solutions for class 12 Physics.
• NCERT solutions for class 12 Chemistry.
• NCERT solutions for class 12 Mathematics.
• NCERT solutions for class 12 Biology.

NCERT Exemplar Solutions Subject wise link:

• NCERT exemplar solutions for class 12 Physics.
• NCERT exemplar solutions for class 12 Chemistry.
• NCERT exemplar solutions for class 12 Mathematics.
• NCERT exemplar solutions for class 12 Biology.