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# CourseNotes.43 - capacitors We can therefore draw the...

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11.4 RL Circuits Figure 32: A simple RL circuit. Lets take a closer look at how an inductor acts in a circuit by considering the simple case of an inductor an a resistor in a circuit series (see ﬁgure 32). We can write down the equation governing such a circuit by using Kirchoﬀ’s loop rule. L di dt + Ri - E = 0 This is a simple diﬀerential equation which we have encountered previously with RC circuits. The solutions to this equation depend on the initial conditions of the circuit. Lets consider the situation in which the circuit initially has no current ﬂowing in it and then the voltage source is turned on. The solution in this case is i ( t ) = E R (1 - e - t/τ L ) where τ L = L R If we consider the case in which the circuit initially has a current ﬂowing and then the voltage source is turned oﬀ, then we must modify our diﬀerential equation by dropping the E term. The solution in this case is i = E R e - t/τ L = i 0 e - t/τ L Notice that, as with capacitors, the same time constant shows up in the rising up and in the decay process. Also notice that the form of the equations is exactly the same as it was with
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Unformatted text preview: capacitors. We can therefore draw the useful analogy: capacitors are to charge as inductors are to current. 11.5 Energy Stored in a Magnetic Field As with capacitors, we are now in a position to talk about the energy stored in a magnetic ﬁeld. We will forgo the hand-wavy derivation and simply quote the results here. The energy stored in a magnetic ﬁeld within a conductor is U = 1 2 Li 2 (40) Note that this is very similar to the energy dissipated by a resistor and to the energy stored in a capacitor. As with capacitors, we can use the idea of energy stored in an inductive magnetic ﬁeld to sneak in the back door of the much broader and more important concept of energy density. The energy density of a magnetic ﬁeld (no matter how it is produced) is u = 1 2 μ B 2 (41) Notice that this is very similar to the energy density of an electric ﬁeld. 43...
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## This note was uploaded on 12/05/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.

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