Electromagnetic Induction And Alternating Current Class 12 Pdf Download
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 =B2l2v / R. The power required to move the conductor with a constant speed is given by P= B2l2v2/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 (M12) is due to change of current in coil 2. (M12 =M21).
â€¢ The self-inductance of a long solenoid is given by L = Î¼0n2Al 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 M12 = M21 = Î¼M0 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.
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 = Io/âˆš2 = 0.707i0 . Similarly, vrms = vo/âˆš2 = 0.707vo.
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=Îµ0SinÏ‰t, applied to a resistor R drives a current I = I0SinÏ‰t in the resistor, I0 = Îµ0 /R where Îµ0& I0 are the peak values of voltage and current. (also represented by Vm & Im)
â€¢ For an AC emf Îµ = Îµm 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 = im Sin (Ï‰t-Ï€/2). Im = Îµm/XL; XL = 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 = ÎµmSinÏ‰t and I= ImSin(Ï‰t+Ï€/2) where Im = Îµm/XC and XC = 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 = ÎµrmsIrmsCosÎ¦
â€¢ In a purely resistive circuit Î¦ = 0; P = VRMSIRMS.
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 XC = XL, so that Z = R and resonant frequency wr
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 = Îµ0SinÏ‰t. Current induced in the coil I = Îµ/R = Îµ0SinÏ‰t/R = I0SinÏ‰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 NS>NP; ÎµS>ÎµP& IS< IP â€“ step up. If NP>NS; ÎµP>ÎµS & IPIS 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
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