EXAMPLE 18.3 Equivalent Resistance GOAL Solve a problem involving both series an

Question

EXAMPLE 18.3 Equivalent Resistance GOAL Solve a problem involving both series and parallel 6.00 resistors PROBLEM Four resistors are connected as shown in figure a 13.00 4.0 (a) Find the equivalent resistance between points a and c a AM (b) What is the current in each resistor if a 42-V battery is connected between a and c? 3.0 STRATEGY R the circuit in steps, as shown in figures b educe and c, using the sum rule for resistors in series and the reciprocal-sum rule for resistors in parallel. Finding the currents is a matter of applying Ohm's law while working 12.0 2.0 backwards through the diagrams. a N 14.00 The four resistors shown in figure a can be reduced in steps to an equivalent 14-n resistor.

Explanation / Answer

a)Req = [ 2+1] + [ 1 / { (1/2) + (1/1) } ]

           = [2+1] + [2*1/(2+1)]

         = 3.667 ohm

b] Total 'I' = V/R = 44/3.667 = 12 A

         I1 = I*R1/(R1+R2)

            = 12*(1/3)

            = 4 A

i2 = I*R2/(R1+R2)

    = 12*2/3

     = 8 A

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