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 2012 J. F. Becker

PREPARATION FOR FINAL EXAM At a minimum the following should be reviewed: Gauss's Law - calculation of the magnitude of the electric field caused by continuous distributions of charge starting with Gauss's Law and completing all the steps including evaluation of the integrals. Ampere's Law - calculation of the magnitude of the magnetic field caused by electric currents using Ampere's Law (all steps including evaluation of the integrals). Faraday's Law and Lenz's Law - calculation of induced voltage and current, including the direction of the induced current. Calculation of integrals to obtain values of electric field, electric potential, and magnetic field caused by continuous distributions of electric charge and current configurations (includes the Law of Biot and Savart for magnetic fields). Maxwell's equations - Maxwell's contribution and significance. DC circuits - Ohm's Law, Kirchhoff's Rules, power, series-parallel combinations. Series RLC circuits - phasor diagrams, phase angle, current, power factor Vectors - as used throughout the entire course.

Learning Goals - we will learn: ch 30 How to relate the induced emf in a circuit to the rate of change of current in the same circuit. How to calculate the energy stored in a magnetic field. Why electrical oscillations occur in circuits that include both an inductor (L) and a capacitor (C).

RL

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 inductor 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

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 = i  V ab P = i L di/dt dU = L i di Energy density of B field is Power = energy / time P =  V ab i = i 2 R U = P t = i 2 R t

RL circuit (similar to an RC circuit)

vs Increasing current vs time for RL circuit.

vs Decreasing current vs 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

Oscillating LC circuit oscillating at a frequency  (radians / second)

An inductor (inductance L) and a capacitor (capacitance C) are connected as shown. If the values of both L and C are doubled, what happens to the time required for the capacitor charge to oscillate through a complete cycle? Q30.7 A. It becomes 4 times longer.B. It becomes twice as long. C. It is unchanged.D. It becomes 1/2 as long. E. It becomes 1/4 as long.

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

Series RLC circuit (switch d-a)

Inductor for Exercise 30.9

See Review C 2012 J. F. Becker