3. Electromagnetism

Definitions

• Mutual Inductance is the principle of transformers where a changing current in primary circuit can induce a voltage into a secondary circuit
• Lenz’s Law states that when the current through an inductor changes the voltage induced in it is in such a direction as to oppose the original change
• Currents circulating in the core are known as eddy currents.
• Impedance matching is the practice of designing the input impedance of an electrical load or the output impedance of its corresponding signal source to maximize the power transfer or minimize signal reflection from the load.

Units of measurement

• Henry is mutual inductance between two coils

Formula

• P (in) = P (out), where P (in) is power in the primary circuit and P (out) is the power in the secondary circuit (assuming no losses)
• Vs / Vp = Ts / Tp where Vs is voltage in secondary circuit, Vp is voltage in the primary circuit, Ts is turns in the secondary circuit, Tp is the turns in the primary circuit
• Voltage generated ∝ rate of change of the magnetic field (faster movement will generate a greater voltage)
• amount of force on a conductor, carrying a current in a magnetic field ∝ to the current flowing
• Impedance ratio = (Turns)²

Notes

Electromagnetism

Voltages induced:

• A voltage is induced across the coil if a magnet is moved into a coil a voltage will be generated
• The voltage will be zero once the magnet is stationary in the coil
• A reverse voltage will be generated when the magnet is withdrawn from the coil

Electricity is produced when:

• magnetic field is moving across the wires of the coil
• magnet could be fixed and the coil is moving across the magnetic field
• relative movement is necessary

Generator

• If a magnet is rotated near or within a coil a voltage will be generated in that coil
• Voltage will not be constant but will vary like a sine-wave
• Voltages:
  • maximum when the end of the magnet passes the coil
  • minimum when it is broadside to the coil
• This will produce Alternating Voltage, which will produce an Alternative Current

Electromagnetic Induction

Moving a magnet into a coil produces a voltage because the magnetic lines of force pass (or cut) through the turns of wire

Mutual induction

• The alternating current in the primary coil produces a changing magnetic field
• The voltage induced into the secondary coil is “up-side down” when compared to the primary current

Self inductance

• Opposition to the change in current is known as self inductance
• An alternating current, as it is changing all the time, finds it very difficult to pass through an inductor
• The higher the AC frequency the higher the opposition

Inductors

• The value of an inductance depends mainly on the number of turns in the coil and the core
• inductance increase by
  • more turns of wire
  • inserting an iron or ferrite core
• inductance reduced by
  • lesser turns
  • removing the ferrous core
  • brass core will actually reduce the inductance below the air core value

Eddy Currents

• If the core of an inductor is able to conduct electricity then it will absorb some of the power and the inductor will be a poor lossy one
• Currents will circulate in the core and are known as eddy currents
• Eddy currents can be prevented by making the core, even metallic, highly resistive.
• Example ferrite, dust iron and laminations

Transformers

• There must be good magnetic coupling between the primary and secondary circuits
• At low frequencies this means that the primary and secondary coils must be wound on the same magnetic core
• Cores constructed of a stack of soft iron laminations that are oxidised to ensure that they are insulated from each other

Matching

• power dissipated in the resistor is then calculated for several values of the variable load resistor
• Maximum power transfer takes place when the load is matched to the source.
• AC resistance of the load should be matched to the AC resistance of the source

Image credit: http://electronicdesign.com/

Moving coil meters

• amount of force on a conductor, carrying a current in a magnetic field, is proportional to the current flowing - assuming that the magnetic field remains constant
• A core is provided to ensure a uniform magnetic field for the coil to rotate in
• Delicate springs are fitted to the top and bottom of the coil to:
  • conduct the current in and out of the coil
  • to provide the opposing force to balance the motor action

Ammeter	Voltmeter
low resistance	high resistance
avoid reducing the current in the circuit under test	take minimum current from the circuit under test
measure as high current as possible	measure as high voltage as possible
by adding a shunt resistor in parallel with the meter	by adding a multiplier resistor in series with the meter

Image credit of ammeter and voltmeter: SARTS