You are given three resistors: two 4 ? resistors and one 6 ? resistor. What is t

Question

You are given three resistors: two 4? resistors and one 6? resistor.
What is the value in Ohms ( ? ) of the largest-valued resistor that can be fabricated by combining these three resistors? What is the value in Ohms ( ? ) of the smallest-valued resistor that can be fabricated by combining these three resistors? Given that each individual resistor can dissipate up to 1 watt of power before burning up, how much total power in watts ( W ) can the smallest-valued composite resistor dissipate before burning up?

Explanation / Answer

Largest is having them all in series: 4+4+6 = 14 smallest is all in parallel: 1/R = 1/4 + 1/4 + 1/6 R= 3/2 in parallell all get same voltage so since power is V^2/R the 4 will get to 1W first when V^2/4 = 1 so V =2 so each 4 using 1 W and the 6 uses 2^2/6 = 2/3 so total power 1+1+2/3 = 8/3 W

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