Question

A particular circuit toolbox contains only 80 Ω resistors and switches, which can be open or closed. Construct a circuit, filling in all four boxes, such that the overall equivalent resistance between A and B is 40 Ω?

Answer 1

Answer:

Here we need to make parallel connection of two 80 ohm resistors to achieve 40 ohm net resistance.

Explanation:

As we know that the resistances in series add up directly and here we are given with only the resistors of 80 Ω.

So when we connect two resistors of 80 ohm in parallel we get the resultant of 40 ohm.

Mathematically:

$\frac{1}{R_p} =\frac{1}{R} +\frac{1}{R}$

$\frac{1}{40} =\frac{1}{R} +\frac{1}{R}$

$\frac{1}{40} =\frac{2}{R}$

$R=80\Omega$ gives us the only combination of two resistors in parallel.