Electromagnetic Induction And Alternating Current Class 12 Pdf Download

Chapter 4 ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENTS

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

â€¢ Magnetic flux through a surface of area A placed in a uniform magnetic field B is defined as CosÎ¸ where Î¸ is the angle between B and A.

â€¢ Magnetic flux is a scalar quantity and its SI unit is weber (Wb).

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

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 Faradayâ€™s law indicates this fact.) Lenz law obeys the principle of energy conservation.

â€¢ 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.

â€¢ The direction of induced current is obtained from Flemingâ€™s right hand rule.

â€¢ 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. Îµ = Blv.If â€˜Râ€™ 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 =B^{2}l^{2}v / R. The power required to move the conductor with a constant speed is given by P= B^{2}l^{2}v^{2}/R.

â€¢ The induced currents produced on the surface of a thick conductor when magnetic flux linked with that changes are called eddy currents.

â€¢ 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. =

â€¢ 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 Îµ = 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).

â€¢ 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.

â€¢ The changing current in a coil can induce an e.m.f in a nearby coil. This
relation, Îµ = shows that Mutual inductance of coil 1 with respect to coil
2 (M_{12}) is due to change of current in coil 2. (M_{12} =M_{21}).

â€¢ The self-inductance of a long solenoid is given by L = Î¼_{0}n^{2}Al 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.

â€¢ The mutual inductance of two co-axial coils is given by M_{12} = M_{21} = Î¼M^{0}
n_{1}n_{2}A_{l} 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.

â€¢ Energy stored in an inductor in the form of magnetic field is and Magnetic energy density

â€¢ The electric current whose magnitude changes continuously and direction
changes periodically is called alternating current (AC). I = Io Sin Ï‰t.
â€¢ 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 = I_{o}/âˆš2 = 0.707i0 . Similarly, vrms = v_{o}/âˆš2 = 0.707v_{o}.

â€¢ 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.

â€¢ 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).

â€¢ An alternating voltage Îµ=Îµ_{0}SinÏ‰t, applied to a resistor R drives a current I =
I_{0}SinÏ‰t in the resistor, I_{0} = Îµ_{0} /R where Îµ_{0}& I_{0} are the peak values of voltage and
current. (also represented by V_{m} & I_{m})

â€¢ For an AC e_{m}f Îµ = Îµ_{m} Sin Ï‰t applied to a resistor, current and voltage are in
phase.

â€¢ In case of an a.c. circuit having pure inductance current lags behind e.m.f by
a phase angle 90Â°. Îµ = Îµm Sin Ï‰t and i = i_{m} Sin (Ï‰t-Ï€/2). I_{m} = Îµ_{m}/X_{L}; X_{L} = Ï‰L is
called inductive reactance.

â€¢ In case of an a.c. circuit having pure capacitance, current leads e._{m}.f by a
phase angle of 90Â°. Îµ = Îµ_{m}SinÏ‰t and I= I_{m}Sin(Ï‰t+Ï€/2) where I_{m} = Îµ_{m}/X_{C} and X_{C} =
1/Ï‰C is called capacitive reactance.

â€¢ In case of an a.c. circuit having R, L and C, the total or effective resistance of the circuit is called impedance (Z).

â€¢ Average power loss over a complete cycle in an LCR circuit is P =
Îµ_{rms}I_{rms}CosÎ¦

â€¢ In a purely resistive circuit Î¦ = 0; P = V_{RMS}I_{RMS}.

â€¢ In a purely inductive circuit Î¦ = Ï€/2; P = 0.

â€¢ In a purely capacitive circuit Î¦ = Ï€/2; P = 0.

â€¢ The electric current in an AC circuit is said to be wattless current when average power dissipated or consumed is zero.

â€¢ In an LCR circuit, the circuit admits maximum current if X_{C} = X_{L}, so that Z
= R and resonant frequency w_{r}

â€¢ The device which converts mechanical energy in to AC electrical energy by virtue of electromagnetic induction is called AC Generator.

â€¢ Rotation of rectangular coil in a magnetic field causes change in flux (Î¦ =
NBACosÏ‰t). Change in flux induces e.m.f in the coil which is given by Îµ= -dÎ¦/dt = NBAÏ‰SinÏ‰t. Îµ = Îµ_{0}SinÏ‰t. Current induced in the coil I = Îµ/R = Îµ_{0}SinÏ‰t/R =
I_{0}SinÏ‰t

â€¢ The device which converts an AC voltage of one value to another is called Transformer. For an ideal transformer,â€¢ In an ideal transformer, ÎµPIP = ÎµSIS. i.e

â€¢ If N_{S}>N_{P}; Îµ_{S>}Îµ_{P}& I_{S}< I_{P} â€“ step up. If N_{P}>N_{S}; ÎµP>Îµ_{S} & I_{P}I_{S} â€“ step down.

â€¢ Losses in transformer: Copper losses; Iron losses, Flux losses; Hysteresis losses; Humming losses.

â€¢ 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

â€¢

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- Chapter 5: Magnetrism And Matter
- chapter 1 ELECTROSTATICS
- Chapter 2 CURRENT ELECTRICITY
- Chapter 3 Agnetic Effects Of Current And Magnetisml
- Chapter 4 ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENTS
- Chapter 5 Electro Magnetic Waves
- Chapter 6 Optics Ray Optics
- Chapter 7 Dual Nature Of Matter & Radiation
- Chapter 8 Atoms & Nuclei
- Chapter 10: Wave Optics
- Chapter 14: Semiconductor Electronics, Materials, Devices and Sample Circuits

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