ELEC ELE TRO TR MAGNETIC INDUCTION

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Sabrina O’Neal’
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1 ELECTRO MAGNETIC INDUCTION

2 Faraday Henry

3 Laws:- Faraday s Laws :- 1) When ever there is a change in magnetic flux linked with a coil, a current is generated in the coil.

4 The current is called induced current and the emf responsible for the current is called induced emf. The phenomenon is called electro magnetic induction.

5 2) The induced emf (the induced current) is directly proportional to the rate of change of magnetic flux. (The emphasis is on the change of flux)

6 Lenz s Law:- The direction of the induced current (induced emf) is always to oppose the cause for which it is due. (Emphasis is on cause)

7 Motional emf, Self induction,mutual induction and Eddy currents. Motional emf = BLv volt. self inductance of a coil is L = µ 2 0 µ r N A (µ r is the relative permeability of the core), µ r = 1for air core

8 Mutual- induction: Between Pair of coils, M = µ 0 µ r N 1 N 2 A henry (µ r is the relative permeability of the core µ r = 1, for air core.)

9 Eddy currents :- They are cyclic currents also called focault current in the bulk of a metal in a direction perpendicular p to the magnetic flux. They cause heating effect and dissipate energy. This can be minimized by using laminated plates.

10 Alternating current (Alternating voltage) The current which oscillates between a positive maximum value and a negative minimum value is called alternating current(ac).the emf responsible is called alternating voltage.

11 V=V V 0 sinωt isthe expression for alt - voltage I = I 0 sinωt is the 0 expression for alt - current 0

12 e 0 and i 0 are the peak (max) values of the induced voltage and induced current respectively. ωt = sin -1 V/ V 0 or ωt = sin -1 I/ I 0 is called the phase. If ωt t is the same for current and voltage, then they are said to be in phase.

13 V ave = ( 2/π)V 0, I ave = ( 2/π)I 0 V rms = V 0, / 2 I rms = I 0 / 2 P rms = V rms I rms P rms = (V 0, / 2 ) X (I 0 / 2) = V 0 I 0 /2 is called half power point in ac circuits

14 AC applied to resistance, ideal inductance and ideal capacitance. Ideal means inherent resistance of the circuit component is not considered for discussion. Power in AC circuits:- it P ac = VI cosφ. V= P D measured. I= Current measured, φ is the phase difference between voltage and current.

15 cosφ φ is called the power factor in AC circuits because the magnitude of power transfer in AC circuits is dictated t d by cosφ.

16 AC applied to resistance The behavior of resistance is identical for both AC and DC (we know that P dc = Voltage x current)

17 The value of resistance is independent of frequency. The voltage and current are always in phase in a resistance. That means, in a purely resistive AC circuit,ie., φ = 0, cos φ =1. P ac = V I watt. In other words For a resistance P dc = P ac

18 The behavior of inductance for DC is transient where as for AC it is perpetual. It offers Inductive reactance X L = ωl =2πfL ohm to AC. X L α f, the frequency of the Applied AC.

19 The applied voltage and the resulting current through the pure inductance are not In phase V = V 0 sin ωt. I = I 0 sin (ωt -90), φ = 90 0

20 The current lags behind the voltage by 90. P ac = VI cos φ = P ac = VI cos 90 P ac = 0 watt The AC through an ideal inductance is called Watt less current.

21 AC The applied behavior to of a capacitance ideal capacitance to DC is instantaneous where it gets charged to the potential of applied DC voltage. When Alternating voltage is applied across C its action becomes perpetual. It offers a capacitive reactance.

22 X c = 1/ωC = (1/2πf C) ohm. ie, X c α 1/f V = V 0 sin ωt I = I 0 sin (ωt + 90) The applied voltage and the resulting current are not in phase. The current leads the voltage by 90.

23 Series RLC circuit Here a resistance, an ideal inductance and an ideal capacitance are connected in series with a plug key. When the key is closed the source drives a current through the series combination and maintains an effective voltage V across the combination.

24 The effective voltage can be obtained by a vector (phasor) obtained by a vector (phasor) diagram. V = {V 2 R + (V L -V C ) 2 } V = I {R 2 + (X L - X C ) 2 }, V/I = Z ohm called the V / I Z ohm called the Impedance ( Effective resistance ff d t AC b th i RLC offered to AC by the series RLC circuit). Z = {R 2 + (X L -X C ) 2 } ohm

25 Series resonant circuit A series RLC circuit connected to an AC source of adjustable frequency (function generator) is called a series resonant circuit. When the circuit is switched on, it drives a current through the circuit. The magnitude of the current depends on the impedance Z.

26 But impedance depends on the values of R, X L and, X C.., R is independent of frequency, X L α f and X C α 1/f. Z = {R 2 + (X L - X C ) 2 } ohm.

27 At low frequencies of the applied AC (X C > > X L ), (X L -X C ) 2 is very large, Z is large and I is small At high frequencies of the applied AC (X L > > X C ), (X L -X C ) 2 is again very large, Z is large I is small.

28 Therefore When frequency increases from a low value to a high value X C decreases, X L increases. At one particular frequency f r, X L = X C, Z = Z min = R. I increases gradually And becomes maximum I = I max at f r.

29 This point of I = I max is called electrical l Resonance and dthat t particular frequency is called resonant frequency f r.

30 Resonant frequency. At f r, XL = XC, Z = R, Power factor Cosφ = R / Z 2π f r L = 1/2π f r C f r = 1/2π (L C) Q factor :- Q = (Voltage across L)/(Voltage across R) at resonance. Q = (V L / V R ) = IX L /IR = X L /R Q = 2π f r L/R But 2π f r = 1/ (L C) Q = (L/R) x (1/ (L C) = [ (L/ C)] x 1/R

31 At half power frequency I = (I max / 2). Band width = f 2 -f 1 and Q = f r /(f 2- f 1 ). Q value is also called the sharpness of resonance or selectivity of the resonance circuit. Q is large when R is small.

32 (1) (2)

33 Transformer For an ideal transformer, (V /V )=(N/N N )=K K is called Transformer turn ratio.

34 K> 1 N >N it is called step up voltage transformer. K< 1 N < N it is called step down voltage transformer. K = 1 N = N it is called buffer transformer (Used in circuit isolation and impedance matching). Input power = out put power V I = V I

Chapter 33. Alternating Current Circuits

Chapter 33. Alternating Current Circuits Chapter 33 Alternating Current Circuits 1 Capacitor Resistor + Q = C V = I R R I + + Inductance d I Vab = L dt AC power source The AC power source provides an alternative voltage, Notation - Lower case