Ex : What is the minimum number of 2 Ohm resistors which has to be connected to have an effective resistance of 1.5 Ohms?

  • $\begingroup$ @pentane : So far I have no idea to solve this question and that's why I posted this message $\endgroup$ – Aathesh Vigram May 1 '18 at 15:51

There are two cases that have to be considered :

$1.$ The total resistance you want to obtain is greater than you already have in your circuit.

In this case you have to add a resistance in series. Seeing how for two resistances connected in series you have : $$R_{tot} = R_{1} +R_{2}$$ you have need to solve a very simple equation and obviously you only need one resistance.

$2.$The total resistance you want is smaller than what you have.

In this case you have to add a resistance n parallel. However this time : $$\frac{1}{R_{tot}} = \frac{1}{R_{1}} + \frac{1}{R_{2}}$$ Again simple equation and you only need one resistance.

Note that while mathematically you can always have an answer, it is possible that the resistance you have calculated is either too small or too big, so practically you may need to incorporate more resistances. In this case things become more complicated.


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