ch32_lecture_notes

ch32_lecture_notes - Chapter 32 Inductance and Circuit...

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Chapter 32 Inductance and Circuit Oscillations In this chapter we will study the properties of inductors (also known as “coils”). Inductors, together with capacitors and resistors are the passive elements of electric and electronic circuits In particular we will study: -The induced emf on an inductor due to the change in the inductor’s current or in the current of an inductor close by -Circuits that contain a battery, a resistor, and an inductor (known as RL-circuits ) - Oscillations of circuits that contain an inductor and a capacitor (known as LC-circuits ) (32-1)
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What happens in the circuit shown below as a function of time when we close the switch S? Ultimately (i.e. if we wait for a long time) the current I reaches the value I = E /R. From the plot of I versus time t it is clear that in general I is depends on t in a complicated way. When the switch S is closed, a time dependent current I(t) flows though the circuit. I(t) creates a time dependent magnetic field B (t) and that field creates a time dependent magnetic flux Φ B (t) (33-2) I R = E
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Self-inductance (symbol: L) The magnetic flux Φ B through an inductor is given by the equation: Φ B = LI The proportionality constant L depends on the geometry of the coil. L is known as the self inductance (or more simple the inductance) of the coil Units of L: Wb/A Henry If the magnetic flux Φ B changes with time t an induced emf appears on the coil according to Faraday’s law: + - I L B L I Φ = (32-4) Self induced emf B dd I L dt dt Φ =− E dI L dt E
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Joseph Henry 1797-1878
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What happens when the magnetic field of one loop creates a magnetic flux in a second loop positioned close by? Φ B (2) = L 2 I 2 + M 21 I 1 (32-5) M Mutual Inductance Units: same as L: Henry Note: M 12 = M 21 M The expressions for the flux become Φ B (1) = L 1 I 1 + MI 2 Φ B (2) = L 2 I 2 + MI 1 Φ B (1) = L 1 I 1 + M 12 I 2
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(32-6) () 11 2 1 12 (1) 1 B B LI MI
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ch32_lecture_notes - Chapter 32 Inductance and Circuit...

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