ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENTS

• The phenomenon of production of induced emf in a conductor when electric flux linked with that changes is called electromagnetic induction.

• Magnetic flux through a surface of area A placed in a uniform magnetic field B is defined as  Cos? where ? is the angle between B and A.

• Magnetic flux is a scalar quantity and its SI unit is weber (Wb).

• Faraday’s laws of induction:

First Law: When magnetic flux linked with the conductor changes, induced emf produces across it.

Second Law:

The magnitude of the induced e.m.f in a circuit is equal to the rate of change of magnitude flux linked with that circuit 

• Lenz law:

The direction of induced current or the polarity of the induced e.m.f is in such a way that it opposes the cause that produces it. (The negative sign in Faraday’s law indicates this fact.) Lenz law obeys the principle of energy conservation.

• The induced current in a closed loop can be produced by changing the

(i) magnitude of B

(ii) area A of the loop

(iii) its orientation in magnetic field.

• The direction of induced current is obtained from Fleming’s right hand rule.

• When a metal rod of length l is placed normal to a uniform magnetic field B and moved with a velocity v perpendicular to the field, the induced e.m.f is called motional e.m.f. It produces across the ends of the rod. ? = Blv.If ‘R’ is the resistance of the metal rod, the induced current is given by I=Blv/R, the force acting on the conductor in the presence of magnetic field (due to drift of charge) is given by F =B2l2v / R. The power required to move the conductor with a constant speed is given by P= B2l2v2/R.

• The induced currents produced on the surface of a thick conductor when

magnetic flux linked with that changes are called eddy currents.

• The phenomenon of production of induced emf in a coil itself when electric

current passing through that changes is called self induction. Self Inductance is the

ratio of the flux linkage to current. = 

• When a current in a coil changes it induces a back e.m.f in the same coil.

The self induced e.m.f is given by ? = where L is the self-inductance of the

coil. It is a measure of inertia of the coil against the change of current through it.

Its S.I unit is henry (H).

• The inductance is said to be one Henry when an emf of one volt induces in a

coil for unit rate of change of electric current through it.

• The changing current in a coil can induce an e.m.f in a nearby coil. This

relation, ? = shows that Mutual inductance of coil 1 with respect to coil

2 (M12) is due to change of current in coil 2. (M12 =M21).

• The self-inductance of a long solenoid is given by L = ?0n2Al where A is the

area of cross-section of the solenoid, l is its length and n is the number of turns

per unit length. 

• The mutual inductance of two co-axial coils is given by M12 = M21 = ?M0

n1n2Al where n1& n2 are the number of turns per unit length of coils 1 & 2. A is the

area of cross-section and l is the length of the solenoids.

• Energy stored in an inductor in the form of magnetic field is and Magnetic energy density

• The electric current whose magnitude changes continuously and direction

changes periodically is called alternating current (AC). I = Io Sin ?t.

• The root mean square value of a.c. may be defined as that value of steady

current which would generate the same amount of heat in a given resistance in a

given time as is done by the a.c. when passed through the same resistance during

the same time. Irms = Io/?2 = 0.707i0 . Similarly, vrms = vo/?2 = 0.707vo. 

• The rotating vectors which represent the varying quantities are called

phasors. The diagram in which the AC voltage and AC currents are represented as

phasors is called phasor diagram.

• The opposition offered by resistor is called resistance (R). The non-resistive

opposition offered by a device is called reactance (X). The combination of

reactance and resistance is called impedance (Z). 

• An alternating voltage ?=?0Sin?t, applied to a resistor R drives a current I =

I0Sin?t in the resistor, I0 = ?0 /R where ?0& I0 are the peak values of voltage and

current. (also represented by Vm & Im)

• For an AC emf ? = ?m Sin ?t applied to a resistor, current and voltage are in

phase.

• In case of an a.c. circuit having pure inductance current lags behind e.m.f by

a phase angle 90°. ? = ?m Sin ?t and i = im Sin (?t-?/2). Im = ?m/XL; XL = ?L is

called inductive reactance. 

• In case of an a.c. circuit having pure capacitance, current leads e.m.f by a

phase angle of 90°. ? = ?mSin?t and I= ImSin(?t+?/2) where Im = ?m/XC and XC =

1/?C is called capacitive reactance.

• In case of an a.c. circuit having R, L and C, the total or effective resistance

of the circuit is called impedance (Z). 

• Average power loss over a complete cycle in an LCR circuit is P =

?rmsIrmsCos?

• In a purely resistive circuit ? = 0; P = VRMSIRMS.

• In a purely inductive circuit ? = ?/2; P = 0.

• In a purely capacitive circuit ? = ?/2; P = 0.

• The electric current in an AC circuit is said to be wattless current when

average power dissipated or consumed is zero.

• In an LCR circuit, the circuit admits maximum current if XC = XL, so that Z

= R and resonant frequency wr 

• The device which converts mechanical energy in to AC electrical energy by

virtue of electromagnetic induction is called AC Generator.

• Rotation of rectangular coil in a magnetic field causes change in flux (? =

NBACos?t). Change in flux induces e.m.f in the coil which is given by ?= -d?/dt = NBA?Sin?t. ? = ?0Sin?t. Current induced in the coil I = ?/R = ?0Sin?t/R =

I0Sin?t

• The device which converts an AC voltage of one value to another is called

Transformer. For an ideal transformer,• In an ideal transformer, ?PIP = ?SIS. i.e

• If NS>NP; ?S>?P& IS< IP – step up. If NP>NS; ?P>?S & IPIS – step down.

• Losses in transformer: Copper losses; Iron losses, Flux losses; Hysteresis

losses; Humming losses.

• When a charged capacitor is allowed to discharge through an inductor,

electrical oscillations of constant amplitude and frequency are produced, which is

called LC oscillations. The charge on capacitor q satisfies the equation of SHM  •