Electromagnetic Induction And Alternating Currents

When the magnetic field varies continuously as a result called electromagnetic induction.

In simple language we say that, whenever the number of magnetic lines of force passing through a circuit changes,EMF is produced in the circuit. If the circuit is closed, a current flows through it. The EMF and the current produced are called induced EMF and induced current and they last only as long as the magnetic flux is changing; this phenomenon is known as electromagnetic induction.

MAGNETIC FLUX:

The number of magnetic field lines passing through the surface when the surface is placed in an external magnetic field is called magnetic flux.

Magnetic flux= BA

From the formula, we can define magnetic flux as the product of the magnitude of the field and the area of the plane.

The SI unit of magnetic flux is Weber(Wb).

If the magnetic field instead of being perpendicular to the plane makes an angle theta with the perpendicular to the plane then the magnetic flux linked with the plane will be equal to the product of the component of the magnetic field perpendicular to the plane and the area of the plane. Thus,

Magnetic flux(fi)= BA cos

here, is the angle between magnetic field and area vector

And A= area present in the magnetic field.

METHODS OF CHANGING MAGNETIC FLUX:

1. By rotating the coil in the magnetic field(i.e. by changing )
2. By changing A
3. By changing magnetic field B

ELECTROMAGNETIC INDUCTION LAWS:

FARADAY’S LAW: Faraday’s law tells about how EMF is generated when electric current quantity is changed through changing the magnetic field.

Faraday’s First Law states that “In any loop, the magnetic field changes continuously with respect to time the EMF is produced in this loop.” 

This is also known as Neumann’s Law.

Faraday’s Second Law states that the magnitude of induced EMF in a circuit is directly proportional to the rate of change of magnetic flux linked with the circuit.

LENZ LAW:

It states that the current induced in a circuit always flows in such a direction where it opposes the change or the course that produces it.

INDUCTANCE:

An electric current may or may not be induced in a coil by a change in flux produced by another coil around it or flux change due to the same coil.

It depends upon the geometry of the coil and Intrinsic material properties.

SELF INDUCTION:

Self-induction is also called electrical inertia. It is a property of the coil by which it opposes any kind of growth or decay of the current in the circuit by producing induced current, also called back EMF in the coil.

MUTUAL INDUCTION:

If we change any strength of current in the first coil induced EMF is developed in another coil, the phenomenon called mutual induction.

ALTERNATING CURRENT:

Alternating current is the current whose magnitude changes with time, and the direction reverses periodically. It varies like a sin function.

Also, alternating EMF changes in magnitude continuously with time and reverses its direction periodically.

AVERAGE OR MEAN VALUE OF CURRENT IN HALF-CYCLE:

Every value of AC(equivalent to DC) is that constant current that flows the same amount of charge in half cycle in the same resistance as done by AC (variable current) in the same time interval.

The average value of current in half cycle is

I(mean value)= 63.6% I

This can be calculated by integration.

ROOT MEAN SQUARE VALUE OF ALTERNATING CURRENT:

• The root mean square value of alternating-current is defined as the square root of the average of I2 during a complete cycle, where I is the instantaneous value of the alternating current.

The RMS value of current is

I(rms)=70.7% I

PHASORS AND PHASOR DIAGRAMS:

The (rotating)vectors representing current and voltage are called ‘phasors’.

A diagram representing alternating current and alternating voltage(of same frequency) as rotating vectors(phasors) with the phase angle between them is called a phasor diagram.

DIFFERENT TYPES OF AC CIRCUIT:

• Circuit containing resistance only

In a pure resistor the current is always in phase with the applied voltage.

• Circuit containing inductance only

In a poor conductor, the current lag behind the voltage by a phase angle of (π/2) or 90°.

• Circuit containing capacitance only

In a pure capacitor, the current leads the voltage by a phase angle of 90°.

• Circuit containing inductance and resistance in series (L-R series circuit)

In the L-R circuit, the applied voltage leads the current.

• Circuit containing capacitance and resistance in series (C-R series circuit)
• Circuit containing inductance and capacitance (L-C circuit)
• Circuit containing inductance capacitance and resistance in series (L-C-R series circuit)

Here we have three cases:

• When L>1/C, then tan is positive, that is, is positive. In this case, the voltage leads the current.
• When L<1/C, then tan is negative, that is is negative. In this case, the voltage lags behind the current.
• When L =1/C, then tan =0, that is =0. In this case, the voltage and the current are in phase.

IMPEDANCE TRIANGLE:

The right angle triangle whose base, hypotenuse and perpendicular is expressed in the terms of resistance and Reactance and impedance of the circuit elements.

WATTLESS CURRENT:

If the resistance in an AC circuit is zero, although current flows in the circuit, yet the average power remains zero, that is, there is no energy dissipation in the circuit. The current in such a circuit is called wattless current.

CONCLUSION:

Electromagnetic induction is the process of generating electric current with the help of a magnetic field. It occurs when there is a magnetic field in an electric conductor moving relative to one another. 

Alternating current is the current whose magnitude changes with time and the direction reverses periodically. 

AC consists of many circuits like LCR circuit CR circuit and Circuit containing only capacitance, a circuit containing only inductance, a circuit containing only resistance.

Alternating current flows through the solenoid producing a change in the magnetic field that will cause electromagnetic induction and electric current to flow in the wire loop.