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CBSE Class 12th Physics Notes: Alternating Current (Part ‒ I)

CBSE class 12 physics chapter wise notes on chapter Alternating Current are available in this article. These notes are important for CBSE class 12 Physics board exam 2017.

Jan 2, 2017 14:00 IST
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CBSE class 12 Physics chapter wise notes (or key notes) on chapter Alternating Current are available in this article. These key notes are important and very helpful for revision purpose before the CBSE board exam.

These notes are based on NCERT textbooks and latest CBSE syllabus for class 12 physics 2017.
The topics covered in these notes are given below:

Alternating Current

Alternating Voltage

Average Value (or Mean Value) of Alternating Current

Average Value (or Mean Value) of Alternating Voltage

Root Mean Square value of Alternating Current

Root Mean Square value of Alternating Voltage

Representation of AC Current and Voltage by Rotating Vectors - Phasors

Different Types of A.C. circuits

AC Circuit containing Resistnace only

AC Circuit containing Inductance only

AC Circuit containing Capacitor only

Charging and Discharging of a Capacitor

The short notes of the chapter are given below

Alternating Current

Electric current whose magnitude and direction reverses periodically with time is known as alternating current.

Instantaneous value of alternating current is given by:

I = Io sin ω t or I = Io cos ω t,

Where Io is the peak value of current ω = 2 π v

CBSE Syllabus for Class 12 Physics 2017

Alternating Voltage

Alternating e.m.f. changes in magnitude continuously changes with time and reverses its direction periodically is known as alternating voltage:

Instantaneous value of alternating e.m.f. is given by:

V = Vo sin ω t or V = Vo cos ω t,

Where Vo is the peak value of current ω = 2 π v

Average Value (or Mean Value) of Alternating Current

The Average value or mean value of alternating current over any half cycle is defined as that value of steady current which would sent the same amount of charge through a circuit in the time of half cycle as is sent by the AC through the same circuit, in the same time.

If Io is the peak value of alternating current and Iavg is the average value of current, then Io and Iavg are related as, Iavg = 0.637 Io

CBSE Class 12th Chemistry Notes: All Chapters

Average Value (or Mean Value) of Alternating Voltage

Average value or mean value of alternating e.m.f. over a half cycle is that value of constant e.m.f. which should same amount of charge through a circuit in the time of half cycle, as is sent by alternating e.m.f. through the same circuit in the same time.

If Vo is the peak value of alternating e.m.f. and Vavg is the average value of e.m.f., then Vo and Vavg are related as, Vavg = 0.637 Vo

Root Mean Square value of Alternating Voltage

The root mean square value of alternating e.m.f. is defined as that value of steady voltage; which would generate the same amount of heat in a given resistance in a given time, as is done by the alternating e.m.f., when applied to the same resistance for the same time.

Root mean square value of alternating current (Vrms)  and maximum value of alternating current (Vo) are related as, Vrms = 0.707 Vo

NCERT Solutions for Class 12 Physics

Root Mean Square value of Alternating Current

Root mean square value of alternating current is defined as that value of steady current, which would generate the same amount of heat in a given time, as is done by the AC, when passed through the same resistance for the same time.

Root mean square value of alternating current (Irms)  and maximum value of alternating current (Io) are related as, Irms = 0.707 Io

Representation of AC Current and Voltage by Rotating Vectors — Phasors

The analysis of an ac circuit is by using a phasor diagram. A phasor is a vector which rotates about the origin with angular speed ω, as shown in the figure given below.

Phasor Diagram Representation

Image Source: NCERT Textbooks

The vertical components of phasors i and v represent the sinusoidally varying quantities v and i. The magnitudes of phasors I and V represent the amplitudes or the peak values im and vm of these oscillating quantities

The projection of voltage and current phasors on vertical axis,

i.e., im sin ωt and vm sin ωt respectively represent the value of current and voltage at that instant.

Different Types of A.C. circuits

AC Circuit containing Resistor only

When an AC is passed through a circuit containing (ideal) resistor only, then, alternating current and alternating e.m.f. are in phase and V = IR

AC Circuit containing Resistnace only

Image Source: NCERT Textbooks

AC Circuit containing Inductor only

AC Circuit containing Inductor only

Image Source: NCERT Textbooks

When AC is passed through a circuit containing (ideal) inductor only, then, alternating current lags behind alternating e.m.f. by a phase angle of π/2.

It represents the effective opposition of the coil to the flow of alternating current. It is denoted by XL.

XL= ωL = 2 π f L

Inductive reactance increases with increase in frequency i.e., XLf

Graph of Inductive Reactance vs frequency

Image Source: NCERT Textbooks

AC Circuit containing Capacitor only

AC Circuit containing Capacitor only: Phasor Diagram

Image Source: NCERT Textbooks

When AC is passed through a circuit containing (ideal) capacitor only then, alternating current leads lead alternating voltage by a phase angle of 90o.

Inductive capacitance:

Effective opposition of the capacitor to the flow of alternating current is known as capacitive reactance. It is denoted by XC

XC = 1/(ω C) = 1/(2 π f C)

Inductive capacitance decreases with increase in frequency i.e., Xc ∝ 1/f

InGraph of Inductive Capacitance vs frequency

Image Source: NCERT Textbooks

Charging and Discharging of a Capacitor
When the capacitor is connected to an ac source, it limits or regulates the current, but does not completely prevent the flow of charge. The capacitor is alternately charged and discharged as the current reverses each half cycle.

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