Inductors 1

1
Inductors 1

• Around a permanent magnet there is a magnetic
  field
• The magnetic field is represented by flux lines
• The magnetic flux (?) is measured in webers (Wb)
• The number of flux lines in a given area is
  called the flux density (B)
• It is found that passing a wire thro a magnetic
  field induces a voltage in the wire
• The same effect is caused by keeping the wire
  still and passing a magnetic field over it
• It is also found that passing a current along a
  wire creates a magnetic field

2
Inductors 2

• Putting the wire into a coil (called an inductor)
  causes this magnetic field to increase and
  wrapping the coil around a ferromagnetic material
  increases the magnetic field further
• The magnetic field of an inductor tries to
  prevent any change in the current
• If the current thro the coil changes the
  inductor creates (temporarily) a voltage which
  opposes the change (Lenzs Law)
• The induced voltage is given by
• vLdi/dt
• The faster the change in current - the greater
  the voltage

3
Inductors 3

• When a dc voltage is applied to a coil it
  initially looks like an open circuit due to
  Lenzs Law and then becomes a short circuit
• The inductance of a coil, measured in henries
  (H), is given by
• LN2uA/l where N is the number of turns
• u is the permeability of the core
• A is the csa of the core
• l is the length of the coil

4
Inductors 4

• Increasing inductance can be obtained by placing
  capacitors in series
• Decreasing inductance can be obtained by placing
  inductors in parallel
• For inductors in series, the total inductance is
  found in the same way as for resistors
• LT L1 L2 L3

5
Inductors 5

• For inductors in parallel, the total inductance
  is found in the same way as for resistors
• 1/LT 1/L1 1/L2 1/L3
• Find the total inductance of these circuits

6
RL and RLC dc Circuits

• For practical purposes an inductor can be
  replaced by a short circuit and a capacitor by an
  open circuit in a dc circuit, after the initial
  transient period
• For the circuits below, find all of the relevant
  voltages and currents.

7
Energy Stored

• The ideal inductor does not dissipate energy - it
  stores it as a magnetic field
• The energy stored by an inductor is given by
• W 0.5 LI2 joules
• Find the energy stored by the inductor when the
  current has reached its final value.