Induced emf and Magnetic Flux F

1
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
• Faradays Law of Induction E -N(D FB/ Dt)
• Lenzs Law An induced emf always gives rise to a
  current whose magnetic field opposes the original
  change in flux

2
emf Induced in a Moving Conductor

• Faradays 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 Faradays 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

3
Transformers and power transmission

• A transformer consists of two coils primary and
  secondary
• Transformer equation I Vs / Vp Ns / Np
• Ns gt Np produces a step-up transformer
• Ns lt 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

4
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

5
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

6
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 secondimpedance matching
• Sometimes, a transformer is used to alter an
  impedance
• Zp/Zs VpIs/VsIp (Np/Ns)2