Chapter 31 Inductance Currents create magnetic fields Changing

Mutual Inductance Magnetic Interaction between two circuits i 1 FB 2 p 212 c

Mutual Inductance: Units [M] = [F]/[I]=(T m 2)/(A) = Henry (H) Depends upon Geometry

Example: Long Solenoid with Length l, area A and N 1 turns surrounded by

Self Inductance Circuit elements of same circuit link magnetically B I p 212 c

Example: Solenoid from previous example p 212 c 31: 6

Inductors Schematic symbol Induced EMF (Lenz’s Law) i + - Switch closes, current increases

Magnetic Field Energy stored in an inductor I p 212 c 31: 8

Energy stored in a magnetic field Uniform Magnetic field -> energy is distributed uniformly

Example: How big an inductor would be required to store 150 k. Wh of

Potential differences across inductors in circuits Vab depends upon rate of change of current

Homework: How do inductors combine in circuits? -in series? Hints: currents are the same,

The R-L Circuit i E L + R + - p 212 c 31:

The L-C Circuit i L + + +q - -q p 212 c 31:

The L-R-C Circuit i + L - R C + + +q - -q

The Driven L-R-C Circuit i + L v(t)= Vcos(wt) - R C + +

Slides: 25

Download presentation

Chapter 31: Inductance Currents create magnetic fields Changing currents create changing magnetic fields Changing magnetic fields induce EMF’s Circuit elements interact magnetically! p 212 c 31: 1

Mutual Inductance Magnetic Interaction between two circuits i 1 FB 2 p 212 c 31: 2

Mutual Inductance: Units [M] = [F]/[I]=(T m 2)/(A) = Henry (H) Depends upon Geometry (Magnetic) material properties p 212 c 31: 3

Example: Long Solenoid with Length l, area A and N 1 turns surrounded by a coil with N 2 turns. A p 212 c 31: 4

Self Inductance Circuit elements of same circuit link magnetically B I p 212 c 31: 5

Example: Solenoid from previous example p 212 c 31: 6

Inductors Schematic symbol Induced EMF (Lenz’s Law) i + - Switch closes, current increases Inductor opposes increase -> opposes battery. Steady current (i constant) -> no EMF. p 212 c 31: 7

Magnetic Field Energy stored in an inductor I p 212 c 31: 8

Energy stored in a magnetic field Uniform Magnetic field -> energy is distributed uniformly p 212 c 31: 9

Example: How big an inductor would be required to store 150 k. Wh of energy using a coil carrying 200 A? Example: What is the energy density associated with the design field strength produced by the magnets for the ill fated SSC? p 212 c 31: 10

Potential differences across inductors in circuits Vab depends upon rate of change of current + a - a i - b - + b i increasing b i decreasing p 212 c 31: 11

Homework: How do inductors combine in circuits? -in series? Hints: currents are the same, EMF’s add -in parallel? Hints: EMF’s are the same, currents add Look at derivation for resistors! p 212 c 31: 12

The R-L Circuit i E L + R + - p 212 c 31: 13

E/R i t=t p 212 c 31: 14

i E L+ R+ - p 212 c 31: 15

Io i t=t p 212 c 31: 16

The L-C Circuit i L + + +q - -q p 212 c 31: 17

p 212 c 31: 18

q Q t i w. Q t p 212 c 31: 19

The L-R-C Circuit i + L - R C + + +q - -q p 212 c 31: 20

p 212 c 31: 21

p 212 c 31: 22

The Driven L-R-C Circuit i + L v(t)= Vcos(wt) - R C + + +q - -q p 212 c 31: 23

p 212 c 31: 24