✤ Alternating Current (A.C): It is the current whose magnitude changes continuously. with time and whose direction is reverse periodically. at any instant

                                               and                  I = Io Sinwt

                                                                       E=Eosinwt                                          Angular freq

                            

                            

     mean, value or Average value of a/c: It is defined as the value of steady current which would send same amount of charge through a circuit in the time       of half cycle (I) as is sent by a/c through the same circuit, in the same time.

                                                                 Iavg = -2I0/pi = -0.637I₀

                                                                                       and

                                                                 Eavg = 0.637Io

    :. ordinary d/c ammeter and d/c voltmeter cannot measure a/c because in a/c they record zero because average current/voltage over of full cycle is         zero.

✤ Root mean square current: It is the value of steady correct which would generate the same amount of heat in a given resistance in a given time, as is

                         done by the ac when passed through the same time.

                                                     Irms = Io/root 2

                                                     Erms = Eo / root 2

                                           Irms = 0.707I0 Erms 0.707Eo

             Alternating currents/voltages are measured by arc ammeter /voltmeter.

             These instruments are called hot wire instruments. They gives virtual values-

              1) E= Eo sinωt

              2) I = Io Sin (wt)

              1) E= Eo sinωt

              2) I = Io Sin (wt-pi/2)

                    XL=2piVL (V= frequency of arc.)

              2)     In D.C. v=0

                             x=0 in this case power become zero and current is called wattless current.

              3)     In inductive circuit, it is the self-induction (induced) emf that opposes the growth as well as decay of current.

              4)      Phase difference b/w E and I is pi/2 Radian.

                                     So Power = 0

  A.C. circuit contain capacitor only:

                   

           E=Eosinwt

      I = Jo Sin (wt+π/2)

      1. Resistance offered by capacitor (Reactance):

      2. In D.C., ν=0 Xc = ∞ i.e in d.c. capacitor blocks the circuit.

      3. phase difference = 90°, Current leads the voltage.

      4. Power = 0, so current is called wattless current.

      1. effective resistance (impedance)

                     Z= √R2+(XL-Xc)2

      2. effective voltage

                     V= √Vr2+(VL-Vc)2

      3. effective current    

                     I = V/Z

      4. phase difference b/w current and voltage

                     tanφ = |XL-Xc|/R

                     tanφ = |VL-Vc|/VR

             1) when X=Xc, tanφ=0 : φ=0 i.e voltage and current in same phase.

             2) when XL>Xc, tanφ is +ve, hence voltage leads the current by φ and circuit act as inductance dominated.

             3) when X₁ and circuit is capacitance dominated.

❈ Resonance

        It is defined as the phenomenon by which amplitude of current/voltage increases, when frequency of external source of

        energy become equal to the natural frequency of oscillating circuit (LCR) for resonance, resistance should be         minimum (z)             for which XL=Xc

                                         and LCR act as ohmic circuit.

        i) at resonance

                     Angular freq w = 1/√LC Rad/sec.

        2) frequency v = 1/2π√LC Hz

        3) Resistance of LCR z = R.

        4) Current Io = E₀/R.

        5) Power P=E₀×I₀

        6) Voltage across L and C Cancel each other due to opposite in phase.

        7) Resonance frequency does not depend on R

        8) The resonance maximum power is dissipated

✤ Q-factor

        It is used to describe the character of resonance or sharpness of resonance.

        It is defined as the ratio of voltage across XL or Xc and voltage across R.

                   1) Q-factor = VL or VC / VR

                   2) Q-factor = 1/R √(L/C)

                   3) Value of Q-factor usually vary from 10 to 100.

                   4) Higher the Q value, the narrower and sharper is the resonance.

                   5) It represent voltage amplification factor.

✤ Power factor: It is defined as the ratio of true power to apparent power.

                                              cosφ = R/Z

                       1. It is always positive, but less than one

                       2. for ohmic cosφ = 1 It is maximum value.

                       3. for circuit containing L or C only it is zero.

                       4. If it is maximum then maximum Power is dissipated in circuit.

               RL CIRCUIT                              RC CIRCUIT                              LCR CIRCUIT

                        

NOTES : 1. ordinary d.c ammeter and d.c voltmeter can't measure Alternating current/voltage, because they record zero reading.

            2. 220V a.c is more dangerous than 220 d.c.

            3. a.c current/voltage are measured by a.c Ammeter/ voltmeter known as hot wire instrument.

NOTES 1. Resistance(R) obstract electron

            2. in inductor, opposition of electron due to induced emf

            3. in capacitor resistance offered by charged capacitor.

            4. R reduces a.c and d.c

            5. L reduces a.c only, 6. C block d.c.

• Energy stored in inductor UB=1/2 LI² is pure magnetic

• Energy stored in capacitor Uc=1/2 Q²/C is pure electric,

Notes: 1. A.C can be converted into d.c by rectifier and d.c can be converted into a.c by inverter.

    2. A.C can be step up or down by transformer, d.c can't.

    3. at t = 0, T/2, T, 3T/2, q=maximum

                Energy is completely stored in C

    4. at t = T/4, 3T/4, 5T/4, q=0

                         Energy is magnetic

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