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Induced emf and Magnetic Flux F. Faraday found that induced emf is produced by a changing magnetic field Constant magnetic field, B, induced NO emf Magnetic flux in weber, F B = BA cos q 1 Wb = 1 T-m 2 Faraday’s Law of Induction: E = -N( D F B / D t)

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induced emf and magnetic flux f
Induced emf and Magnetic Flux F
  • Faraday found that induced emf is produced by a changing magnetic field
  • Constant magnetic field, B, induced NO emf
  • Magnetic flux in weber, FB = BA cos q
  • 1 Wb = 1 T-m2
  • Faraday’s Law of Induction: E = -N(D FB/ Dt)
  • Lenz’s Law: An induced emf always gives rise to a current whose magnetic field opposes the original change in flux

Physics 21: Electromagnetic Induction and AC Circuits - Christopher Chui

emf induced in a moving conductor
emf Induced in a Moving Conductor
  • Faraday’s law: E = -D FB/ Dt = B DA/ Dt = Blv
  • A changing magnetic flux produces an electric field
  • E = F/q = qvB/q = vB
  • AC generator is based on Faraday’s law. It is also called a dynamo or an electric generator
  • E = Blv = NBAw sin wt where w = 2pf
  • A DC generator is like an ac generator except the slip rings are replaced by split-ring commutators
  • Cars use ac generators or alternators
  • Counter emf or back emf is a result of Lenz’ law
  • Opposing the change in B, eddy currents are produced

Physics 21: Electromagnetic Induction and AC Circuits - Christopher Chui

transformers and power transmission
Transformers and power transmission
  • A transformer consists of two coils: primary and secondary
  • Transformer equation I: Vs / Vp = Ns / Np
  • Ns > Np produces a step-up transformer
  • Ns < Np produces a step-down transformer
  • Transformer equation II: Is / Ip = Np / Ns
  • Transformers help power transmission
  • Microphones use the principle of induction
  • During recording, the audio or video signal voltage is sent to the recording head, acting like an electromagnet. Playback is opposite to recording

Physics 21: Electromagnetic Induction and AC Circuits - Christopher Chui

mutual inductance and lr circuit
Mutual Inductance and LR Circuit
  • E1 = -M(D I2/ Dt) and E2 = -M(D I1/ Dt) where M is mutual inductance
  • The unit for M is henry, H. 1 H = 1 W-s
  • For a single coil, E = -L(D I/ Dt) where L is self-inductance or simply inductance, or choke
  • The energy stored in a magnetic field = U = ½ LI2
  • The energy density in a magnetic field, u = ½ B2/mo
  • In a LR circuit, I = (V/R) (1- e-t/t) where t = L/R is the time constant
  • Imax = V/R and I = Imax e-t/t

Physics 21: Electromagnetic Induction and AC Circuits - Christopher Chui

ac circuits and impedance
AC Circuits and Impedance
  • I = Io cos 2pft ; Irms = Io/sqrt 2 and Vrms = Vo/sqrt 2
  • For a resistor, both current and voltage are in phase
  • In an inductor, the current lags the voltage by 90o
  • V = IXL and XL = 2pfL is the inductive reactance
  • In a capacitor, the current leads the voltage by 90o
  • V = IXC and XC = 1/2pfC is the capacitive reactance
  • Only R (not C or L) dissipates energy
  • LRC series ac circuit: V = Vo cos(2pft + f) voltage out of phase with current by f; cos f is the power factor
  • Vrms = IrmsZ or Vo = IoZ and tan f = (XL-XC)/R
  • Z = sqrt [R2 +(XL – XC)2] = sqrt [R2 + (2pfL - 1/2pfC)2]

Physics 21: Electromagnetic Induction and AC Circuits - Christopher Chui

resonance and oscillators
Resonance and Oscillators
  • Resonant freq of the circuit, fo = 1/(2p) [sqrt (1/LC)]
  • An LC circuit oscillates and is used as an oscillator
  • Maximum power is transmitted when the output impedance of one device equals the input impedance of the second—impedance matching
  • Sometimes, a transformer is used to alter an impedance
  • Zp/Zs = VpIs/VsIp = (Np/Ns)2

Physics 21: Electromagnetic Induction and AC Circuits - Christopher Chui