Hello! The diagram below is asking to determine the value of all the resistors,

Question

Hello!

The diagram below is asking to determine the value of all the resistors, given the total resistance is 7.2k-ohms. The resistors are all the same value (R1) and the answer should be 12k-ohms. I keep trying to determine how they came up the answer. I tried several methods, and my problem is probably distinguishing where it should be in series or parallel. Could someone please help me understand when and where they are in series and in parallel, as well as show how they got the 12k-ohms? That would greatly help with the rest of my hw! Thanks!

Explanation / Answer

Given Total Resistence = 7.2 K

Find Total Resistence according to the given Circuit

thus

first R1 and R1 are parllel thus = R1*R1 / R1+R1 = R1^2 / 2R1 = R1/2

net R1/2 in seires with R1 thus   R1+R1/2 = 3R1/2

now 3R1/2 and R1 are parllel thus

Equaivalent Resistence = 3R1/2 * R1 / (3R1/2+R1) = 3R1^2 / 3R1+2R1 = 3R1/5

but this given as 7.2 K

thus

3R1/5 = 7.2K

R1 = 7.2 *5 / 3 = 2.4 *5 = 12 K    thus ans.

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