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48. (a) Voltage is proportional to inductance (by Eq. 30-35) 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. 27-21 for resistors. We note that this condition on the currents implies di t dt di t dt di t dt 12 bg += . Thus, although the inductance equation Eq. 30-35 involves the rate of change of current, as opposed to current itself, the conditions that led to the parallel resistor formula also
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