Mutual Inductance (sec. 30.1) Self-inductance and inductors (sec. 30.2) Magnetic field energy (sec. 30.3) RL circuit (sec. 30.4) LC circuit (sec. 30.5) RLC series circuit (sec. 30.6)

Inductance Ch. 30

C 2009 J. Becker

The current i1 in coil #1 gives rise to a flux

through coil #2. If i1 changes, an emf is

induced in coil #2 (and vice versa) according to

Faraday’s Law:

MUTUAL INDUCTANCE

C 2004 Pearson Educational / Addison Wesley

where MUTUAL INDUCTANCE is

An inductor (L) – When the current in the circuit changes the flux changes, and a self-induced emf appears in the circuit. A self-induced emf always opposes the change in the current that produced

the emf (Lenz’s law).

SELF-INDUCTANCE (L)

Across a resistor the potential drop is always from a to b. BUT across an inductor an increasing current causes a potential drop from a to b; a decreasing

current causes a potential rise from a to b.

(a) A decreasing current induces in the conductor an emf that opposes the decrease in current.

(b) An increasing current induces in the inductor an emf that opposes the increase. (Lenz’s law)

c. Physics, Halliday, Resnick, and Krane, 4th edition, John Wiley & Sons, Inc. 1992.

A resistor is a device in which energy is irrecoverably dissipated.

Energy stored in a current-carrying inductor can be recovered when the current decreases to zero and the B field collapses.

P = Vab i = i L di/dt

dU = L i di

Energy density of B field is

Power = energy / time

P = Vab i = (i R) i = i 2 R U = i 2 R (time)

RL circuit

Increasing current vsvs time for RL circuit.

Decreasing current vsvs time for RL circuit.

Oscillation in an LC circuit. Energy is

transferred between the E

field of the capacitor and the B field of the inductor.

Oscillation in an LC circuit.

Energy is transferred between the E field and the B field.

c. Physics, Halliday, Resnick, and Krane, 4th edition, John Wiley & Sons, Inc. 1992.

Oscillating LC circuit oscillating at a

frequency (radians / second)

q(t) vs time for damped oscillations in a series RLC circuit with initial charge Q.

Series RLC circuit

Inductor for Exercise 30.7

Series RL circuit for Exercises 30.69, 30.70, 30.75

RL circuit for Exercises 30.71 and 30.72

Circuit for Challenge Problem 30.78

See www.physics.edu/becker/physics51

Review

C 2009 J. Becker