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CHAPTER 2 Electric Current. Ohm s Law
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Now let RT be the total resistance as seen by the battery in Fig. 28. Then, by Ohm s law, it has to be true that I V RT 31
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Since the left-hand sides of the last two equations are equal, the two right-hand sides are also equal. Setting the two right-hand sides equal, then canceling the Vs, gives 1 1 1 1 1 RT R1 R2 R3 Rn
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where RT is the total e ective resistance seen by the battery. In words, eq. (32) says that If n resistances are connected in parallel, in the manner of Fig. 28, the reciprocal of the total resistance is equal to the sum of the reciprocals of the individual resistances. The power input to each resistance in the parallel-connected circuit of Fig. 28 is (by eqs. (15), (16), (17)) found by any of the formulas
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2 Pn VIn V 2 =Rn In Rn
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where V is the battery voltage, and In is the current in resistor Rn . The total power output P of the battery is given by eqs. (25) and (26), where I is the battery current and where, now, RT is found by means of eq. (32). The following example will be helpful. Example
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In Fig. 29, the battery voltage is V 65 volts, and the values of the resistances, in ohms, are 38, 17, and 27, as shown.
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Fig. 29 In Fig. 29 we wish to nd the following values: (a) total resistance seen by the battery, (b) current measured by the ammeters shown in the gure, (c) power output of the battery, (d) power input to each resistor.
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CHAPTER 2 Electric Current. Ohm s Law