P31_044 - Therefore 1 L eq = 1 L 1 1 L 2(b To ensure the...

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44. (a) Voltage is proportional to inductance (by Eq. 31-37) just as, for resistors, it is proportional to resistance. Now, the (independent) voltages for parallel elements are equal ( V 1 = V 2 ), and the currents (which are generally functions of time) add ( i 1 ( t )+ i 2 ( t )= i ( t )). This leads to the Eq. 28- 21 for resistors. We note that this condition on the currents implies di 1 ( t ) dt + di 2 ( t ) dt = di ( t ) dt . Thus, although the inductance equation Eq. 31-37 involves the rate of change of current, as opposed to current itself, the conditions that led to the parallel resistor formula also applies to inductors.
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Unformatted text preview: Therefore, 1 L eq = 1 L 1 + 1 L 2 . (b) To ensure the independence of the voltage values, it is important that the inductors not be too close together (the related topic of mutual inductance is treated in § 31-12). The requirement is that the Feld of one inductor not have signiFcant influence (or “coupling”) in the next. (c) Just as with resistors, 1 L eq = ∑ N n =1 1 L n ....
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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