Question

Which combination of seven identical resistors of each 2ohm gives rise to the resultant of 10 by 11 ohm

Answer 1

Answer:

Well, an interesting little teaser.

First, lets rule out the series connections. the total effective resistance is less than the individual resistance, so the resistors are in parallel. But there are many parallel arrangements. What to do?

Lets start small. Assume a two branch circuit. One branch hold x resistors in series and another branch has (7-x) in series. The effective resistance can be given by:

Reff=(12x+1(7−x)∗2)−1Reff=(12x+1(7−x)∗2)−1

Replacing x with 1,2… etc quickly reveals this configuration wont work. Lets try a three brach system.

R_eff = (12x+12y+1(7−x−y)∗2)−1(12x+12y+1(7−x−y)∗2)−1

Placing x = 1 and y = 1 gives the correct result R_eff = 10/11.

So the configuration is a three branch parallel circuit, where one branch has 1 resistor, the second also has one resistor and the third has 5 resistor in series..