Electromagnetic Induction and Alternating Current Chapter - Physics JEE Main

JEE Main Physics Chapters 

1

Units and Measurement

11

Electrostatics

2

Kinematics

12

Current Electricity

3

Laws of Motion

13

Magnetic Effects of Current and Magnetism

4

Work, Energy and Power

14

Electromagnetic Induction and Alternating Currents

5

Rotational Motion

15

Electromagnetic Waves

6

Gravitation

16

Optics

7

Properties of Solids and Liquids

17

Dual Nature of Matter

8

Thermodynamics

18

Atoms and Nuclei

9

Kinetic Theory of Gases

19

Electronic Devices

10

Oscillations and Waves

20

Communication Systems

Name of the Concept

Key Points of the Concept

1. Electromagnetic Induction

• Electromagnetic induction is a fundamental concept in physics that describes the generation of an electromotive force (emf) or voltage in a conductor due to a change in magnetic flux linked with it. It is governed by Faraday's law and Lenz's laws.

2. Faraday’s Law of electromagnetic induction

• According to the first law of electromagnetic induction, whenever the magnetic flux linked with the coil changes(ɸ) changes with time(t), an emf is induced in it.

• According to the second law of electromagnetic induction, the induced emf is directly proportional to the rate of change of magnetic flux.

$e\varpropto \dfrac{d\phi}{dt}$

3. Lenz’s law

• Lenz’s law gives the direction of induced current or induced emf and it is based on the law of conservation of energy

• Lenz’s law states that the direction of induced emf or induced current is in such a way that it opposes the cause that produces it.

$e=- \dfrac{d\phi}{dt}$ 

• The minus shows that the induced emf opposes the change in magnetic flux.

4. Eddy Currents

• Eddy currents are circulating currents induced in a conductor when it is exposed to a changing magnetic field. These currents can result in energy losses in electrical devices and are commonly minimized through the use of laminated cores in transformers and motors.

5. Motional emf

• Consider a conductor rod of length l moving with a velocity (v) perpendicular to the uniform magnetic field (B). Then the motional emf induced in the conductor is given by,

$e=Blv$

(Image will be uploaded soon)

6. Self Induction and Mutual Induction

• Due to self-induction, an emf is induced in the coil whenever there is a change in current in the coil. The emf induced in the coil is given b,

$e=- L\dfrac{di}{dt}$

• Sefl inductance(L) is the property of the coil to resist the change in current in the coil and its unit is Henry(H)

(Image will be uploaded soon)

• Due to mutual induction, an emf is induced in the secondary coil due to the change in current in the first coil.

$E_2=- M\dfrac{dI_1}{dt}$

• Coefficient of mutual inductance (M) depends on both coils

7. Alternating Currents

• In alternating current (AC) circuits, the direction of current periodically reverses. AC is characterized by its amplitude, frequency, and phase.

8. Peak and RMS Value of Alternating Current/Voltage

• Peak Value (Imax or Vmax): It is the maximum value reached by the alternating current or voltage during one complete cycle.

• RMS Value (Irms or Vrms): The root-mean-square value represents the equivalent steady direct current or voltage that produces the same heating effect in a given resistor.

9. Combination of Inductance

• When two coils having inductances L1 and L2 are connected in series and mutual inductance is neglected, then equivalent inductance is given by the formula,

$L_{eq}=L_1+L_2$

• If the mutual inductance is considered, then

$L_{eq}=L_1+L_2\pm 2M$

• If two inductances are connected in parallel, then

$\dfrac{1}{L_{eq}}=\dfrac{1}{L_{1}}+\dfrac{1}{L_{2}}$

10. Growth current in LR circuit

• When the switch is closed at t=0, then-current through the inductor at any time is given by,

$I=I_0(1-e^{\dfrac{-t}{\tau}})$

• The steady current (I0) is the maximum constant  current passing through the current after some time.

• The value of the time constant is given by,

$\tau=\dfrac{L}{R}$

11. Purely resistive, capacitive and inductive AC circuits

• The power in an AC circuit is given by P = VIcos(θ), where V is the voltage, I is the current, and θ is the phase angle between them.

• For a purely resistive circuit, voltage and current are in the same phase.

$V=V_0\sin(\omega t)$

$I=I_0\sin(\omega t)$

Where V0 and I0 are the peak voltage and current respectively with angular frequency ⍵

• Power dissipated in the purely resistive circuit is given by,

$P=V_{rms}\cdot I_{rms}$

• For purely inductive circuit, the current is lagging behind the voltage by 900.

$V=V_0\sin(\omega t)$

$I=I_0\sin(\omega t-\dfrac{\pi}{2})$

• Power dissipated in the purely inductive circuit is zero

• For a purely capacitive circuit, the current is leading the voltage by 900.

$V=V_0\sin(\omega t)$

$I=I_0\sin(\omega t+\dfrac{\pi}{2})$

• Power dissipated in a purely capacitive circuit is zero

Er

12. Inductive reactance and capacitive reactance

• Inductive reactance(xL) is the resistance offered by an inductor against the AC current.

$X_L=L\omega $

• Capacitive reactance(xC) is the resistance offered by a capacitor against the AC current.

$X_C=\dfrac{1}{C\omega} $

13. Series RLC circuit

• In a series RLC circuit, resistor, capacitor and inductor are connected in series.

$V=V_0\sin(\omega t)$

$I=I_0\sin(\omega t-\phi )$

• Power factor of the series RLC circuit is the cosine of the phase difference between the voltage and current.

$\text{power factor}=\cos\phi=\dfrac{R}{Z}$

$\cos\phi=\dfrac{\text{Apparent power}}{\text{True power}}$

• Impedance (Z) is the opposition or resistance offered by the RLC circuit against AC current

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

14. Resonance in series RLC circuit

• The current in the RLC circuit becomes maximum when the inductive reactance and capacitive reactance are equal. 

• The formula for resonance frequency is given by,

$f=\dfrac{1}{2\pi\sqrt{LC}} $

• At resonance, the impedance of the RLC circuit becomes equal to the resistance of the circuit.

15. Wattless Current

• Wattless current is the current that lags or leads the voltage in an AC circuit due to the presence of inductive and capacitive components. It does not contribute to real power (watts) but affects the power factor.

16. AC Generator and Transformer

• AC Generator: It is a device that converts mechanical energy into electrical energy by electromagnetic induction. The key component is a rotating coil in a magnetic field.

• Transformer: A transformer is an electrical device that changes the voltage level of an AC signal. It consists of two coils, a primary and a secondary, with mutual inductance.

Sl. No

Name of the Concept

Formula

1.

Emf induced in a coil rotating in a magnetic field(B)

$e=\text{NBA}\omega \cos (\omega t)$

Where N is the number of turns, A is the area of cross-section and ⍵ is the angular velocity of the rotational motion of the coil

2.

Self-inductance of a solenoid having a length (l) and N number of turns

$L=\dfrac{\mu_0N^2A}{l} $

3.

Self-inductance of a circular coil having radius R

$L=\dfrac{\mu_0\pi N^2R}{2} $

4.

Frequency of LC oscillation

$f=\dfrac{1}{2\pi\sqrt{LC}} $

5.

Energy stored in an Inductor 

$E=\dfrac{1}{2}LI^2 $

6.

RMS current and RMS voltage

$I_{rms}=\dfrac{I_0}{\sqrt{2}}$

$V_{rms}=\dfrac{V_0}{\sqrt{2}}$

7.

Relation between mutual inductance and self inductances of two coils

$M=K\sqrt{L_1L_2}$

Where k is the coupling factor

8.

Quality factor of a series resonance circuit

The quality factor is a measure of the selectivity of resonance in an LCR circuit. It is defined as

$Q=\dfrac{L\omega_0}{R} $

$Q=\dfrac{1}{C\omega_0R} $

9.

Transformer ratio

$K=\dfrac{N_s}{N_p} $

$K=\dfrac{V_s}{V_p} $

JEE Main Electromagnetic Induction and Alternating Current Study Materials

JEE Main Electromagnetic Induction and Alternating Current Notes

JEE Main Electromagnetic Induction and Alternating Current Important Questions

JEE Main Electromagnetic Induction and Alternating Current Practice Paper

JEE Main Physics Study and Practice Materials

JEE  Main Physics Previous Year Question Papers

JEE Main Physics Mock Test

JEE Main Physics Formula

JEE Main Sample Paper

JEE Main Physics Difference Between