chapter32

chapter32 - Chapter 32 c Inductance L and the stored...

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Unformatted text preview: Chapter 32 c Inductance L and the stored magnetic energy c RL and LC circuits c RLC circuit Resistance, Capacitance and Inductance Ohm’s Law defines resistance: V R I Δ ≡ Capacitance, the ability to hold charge: Q C V Δ ≡ 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 Δ Δ = ⋅ = = ( ) 2 2 1 1 2 2 E Q U C V C Δ Δ = = 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 μ = When this magnetic field flux changes, it induces an emf, E L , called self-induction: ( ) ( ) 2 B L d NAB d NA nI d dI dI n V L dt dt dt dt dt μ Φ μ = - = - = - = - ≡ - E or: L dI L dt ≡ - 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 μ = 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 ≡ - 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 c The SI unit for inductance is the henry (H) c Named for Joseph Henry: c 1797 – 1878 c American physicist c First director of the Smithsonian c Improved design of electromagnet c Constructed one of the first motors c Discovered self-inductance A s V 1 H 1 ⋅ = Discussion about Some Terminology c Use emf and current when they are caused by batteries or other sources c Use induced emf...
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chapter32 - Chapter 32 c Inductance L and the stored...

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