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**Unformatted text preview: **Chapter 32 Inductance L and the stored magnetic energy RL and LC circuits RLC circuit Resistance, Capacitance and Inductance Ohms Law defines resistance: V R I Capacitance, the ability to hold charge: Q C V Capacitors store electric energy once charged: Resistors do not store energy, instead they transform electrical energy into thermo energy at a rate of: 2 2 V P V I I R R = = = ( 29 2 2 1 1 2 2 E Q U C V C = = Inductance, the ability to hold current (moving charge). Inductors store magnetic energy once charged with current, i.e., current flows through it. Inductance, the definition I When a current flows through a coil, there is magnetic field established. If we take the solenoid assumption for the coil: E E L + B nI = When this magnetic field flux changes, it induces an emf, E L , called self-induction: ( 29 ( 29 2 B L d NAB d NA nI d dI dI n V L dt dt dt dt dt = - = - = - = -- E or: L dI L dt R- E This defines the inductance L , which is constant related only to the coil. The self- induced emf is generated by current flowing though a coil. According to Lenz Law, the emf generated inside this coil is always opposing the change of the current which is delivered by the original emf. For a solenoid: 2 L n V = Where n : # of turns per unit length. N : # of turns in length l . A : cross section area V : Volume for length l . Inductor We used a coil and the solenoid assumption to introduce the inductance. But the definition holds for all types of inductance, including a straight wire. Any conductor has capacitance and inductance. But as in the capacitor case, an inductor is a device made to have a sizable inductance. L L dI dt R- E An inductor is made of a coil. The symbol is Once the coil is made, its inductance L is defined. The self-induced emf over this inductor under a changing current I is given by: L dI L dt = - E Unit for Inductance The SI unit for inductance is the henry (H) Named for Joseph Henry: 1797 1878 American physicist First director of the Smithsonian Improved design of electromagnet Constructed one of the first motors Discovered self-inductance A s V 1 H 1 = Discussion about Some Terminology Use emf and current when they are caused by batteries or other sources...

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