Inductance Chapter 30 mutual inductance self-inductance magnetic-field energy R-L circuits L-C circuits L-R-C circuits 1 5/CircuitiE.html A straight wire has little inductance. Coil the wire an inductance increases. A change in current in a coil induces an emf in an adjacent coil Only time varying currents can induce and emf astr.gsu.edu/hbase/magnetic/indcur.html

Mutual Inductance Potential induced in Coil-2 Flux in Coil-2 is proportional to the current in Coil-1, M 12 is the mutual inductance Assumed that magnetic material has a constant K m, so flux is directly proportional to current and M 21 only depends on geometry Even when the coils are not symmetric: M=Henry= 1Wb/A 2 Derivative with time

Mutual inductance—examples 3 M = mutual inductance is proportional to the of the turns N 1 N 2

Self-inductance 4

5 Self-Inductance and Inductors where L is the inductance in Henries  =

Self-induced emf opposes changes in current Self-inductance, L, depends upon on size, shape, and turns, N For N turns close together, L is proportional to N 2 L depends upon magnetic material If the core is not air, For soft iron K m =5000 producing an L 5000 times greater than an air-core coil Ferromagnetic material produce s L that are not totally linear with current 6

7 Real Inductor is a combination of L and R V ab + – Ideal Inductor + – V ab Real Inductor c

8 i t Inductor Current and Voltage in an Inductive Circuit Current can not change instantaneously v ab t Inductor i t v ab t t0t0 t0t0 Inductor impossible  Theoretically the voltage can change instantaneously

9 Inductance (Chapter 30) Example 30-3 and 30-4Calculating Self-Inductance and Induced EMF Figure 30-8 Toroidal Solenoid N = 200 turns A = 5.0 cm 2 = 5.0 x m 2 r = 0.1 m i increases uniformly from 0 to 6.0 A in 3.0  sec. Determine L Determine the magnitude and direction of the induced emf (  ) K m = 1

Inductance Application –A charged coil can create a field that will induce a current in a neighboring coil. –Inductance can allow a sensor to trigger the traffic light to change when the car arrives at an intersection. Circuit counts how many cars pass over the coil (how many changes in inductance). –Bikes may not trigger circuit –Drive back and forth in crease the car count? 10

11 Inductance (Chapter 30) The RL Circuit (30.4) Figure Figure Increasing Current (S1 closed and S2 open) Figure Decreasing Current (S1 open and S2 closed) 0.37I I

12 Details of current growth in an R-L circuit Take exponent of both sides

13 Details of current growth in an R-L circuit -continued Decay current

R-L circuit current decay Current thru L reaches I 0 and S1 opens and S2 closes 14

L-C oscillating circuit Consider Figure

L-C Circuit 16

Mechanical Analog 17 Mechanical Analog L  m mass 1/C  k spring constant

18 Inductance (Chapter 30) Energy Stored in an Inductor (30.3) Figure 30-9 joules where w = energy stored in inductor i = current in inductor in amperes (30.9)

L-R-C Circuit 19

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