1 / 9

Chapter 32

Chapter 32. Inductance. Outline. Self-inductance (32.1) Mutual induction (32.4) RL circuits (32.2) Energy in a magnetic field (32.3) Oscillations in an LC circuit (32.5) The RLC circuit (32.6, 33.5). Self inductance.

ally
Télécharger la présentation

Chapter 32

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 32 Inductance PHY 1361

  2. Outline • Self-inductance (32.1) • Mutual induction (32.4) • RL circuits (32.2) • Energy in a magnetic field (32.3) • Oscillations in an LC circuit (32.5) • The RLC circuit (32.6, 33.5) PHY 1361

  3. Self inductance • Self induction: the changing flux through the circuit and the resultant induced emf arise from the circuit itself. The emf L set up in this case is called a self-induced emf. • L = -L(dI/dt) • L = - L/(dI/dt): Inductance is a measure of the opposition to a change in current. • Inductance of an N-turn coil: L = NB/I; SI unit: henry (H). Due to self-induction, the current in the circuit does not jump from zero to its maximum value instantaneously when the switch is thrown closed. PHY 1361

  4. Mutual induction • Mutual induction: Very often, the magnetic flux through the area enclosed by a circuit varies with time because of time-varying currents in nearby circuits. This condition induces an emf through a process known as mutual induction. • An application: An electric toothbrush uses the mutual induction of solenoids as part of its battery-charging system. PHY 1361

  5. RL circuits • An inductor: A circuit element that has a large self-inductance is called an inductor. • An inductor in a circuit opposes changes in the current in that circuit. • A RL circuit: • Kirchhoff’s rule: • Solving for I: I = (/R)(1 – e-t/) •  = L/R: time constant of the RL circuit. • If L  0, i.e. removing the inductance from the circuit, I reaches maximum value (final equilibrium value) /R instantaneously. PHY 1361

  6. Energy in a magnetic field • Energy stored in an inductor: U = (1/2)LI2. • This expression represents the energy stored in the magnetic field of the inductor when the current is I. • Magnetic energy density: uB = B2/20 • The energy density is proportional to the square of the field magnitude. PHY 1361

  7. Oscillations in an LC circuit • Total energy of the circuit: U = UC + UL = Q2/2C + (1/2)LI2. • If the LC circuit is resistanceless and non-radiating, the total energy of the circuit must remain constant in time: dU/dt = 0. • We obtain • Solving for Q: Q = Qmaxcos(t + ) • Solving for I: I = dQ/dt = - Qmaxsin(t + ) • Natural frequency of oscillation of the LC circuit: PHY 1361

  8. Oscillations in an LC circuit-from an energy point of view PHY 1361

  9. The RLC circuit • The rate of energy transformation to internal energy within a resistor: dU/dt = - I2R • Equation for Q: • Compare this with the equation of motion for a damped block-spring system: • Solving for Q: Q = Qmaxe-Rt/2Lcos(dt) PHY 1361

More Related