PHY132_L21 - Classical Physics II Classical Physics II...

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Classical Physics II PHY132 Lecture 21 AC Ci it AC Circuits Lecture 21 1 03/19/2010
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Self Inductance Wh M l I d d ib h ff f Whereas Mutual Inductance describes the effect of a changing current in one coil on another coil, there is also an induced EMF in the first coil ITSELF! That is (or should be) completely expected: a coil carrying a changing current , itself experiences the changing flux as well and thus should itself experience a self-induced EMF well, and thus should itself experience a self induced EMF… – the self-induced EMF implies the existence of a voltage difference Δ V between the terminals of the coil … • that opposes the original current change Taking the definition of mutual inductance , we can easily define the SELF-INDUCTANCE L : where E 1 is the self-induced EMF due to the changing 1 1 coil di V dt     E L (Note the "symbolic" sign!) Lecture 21 2 self induced EMF current i 1 03/19/2010
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Series E LR Circuit I iti ll it h S i S Initially, switch S is open; at time t= 0 the switch is closed Kirchhoff’s Rule #2 in this circuit: L E i ( t ) 0 di L iR dt E R t t dt 0 di V iR L dt 0 1 L di V iR dt ( ) i t Ldi ( ) i t L di 0 ( ) V R i t L dx 0 ( ) l V R i t L 0 0 0 ( ) t L R V V i t e 0 0 V iR 0 0 / R V R i 0 V R R x   0 ln R V R   0 ( ) 1 t L R V i t e 0 ( ) t L R L di L V t V e Equivalently: the Voltage across the resistor: ( ( ) ) R V i t R t R R R i d t 0 1 t L R V e the quantity L/R has units ·s/ = time and is the “ Characteristic Time Constant of the LR circuit…
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