Question

Suppose you have a box of identical resistors. Each resistor in the box has a resistance of 20 Ohms. Explain how to connect them together so the total resistance of the network is 25 Ohms. Use the minimum number of resistors in your design.

Answer 1

By using 4 resistors in parallel and followed by a resistor in series.

Step-by-step explanation:

Let consider 5 resistors with a resistance of 20 ohms each, the total resistance is equal to 25 ohms when the first four resistance are settled in parallel and is followed by a resistor is series. The calculations are presented below:

1st Stage (4 resistors in parallel)

`R_(eq,1) = (1)/((1)/(R_(1))+(1)/(R_(2) )+(1)/(R_(3))+(1)/(R_(4)))`

If
`R_(1) = R_(2) = R_(3) = R_(4) = 20\,\Omega`, then:

`R_(eq,1) = (1)/((1)/(20\,\Omega)+(1)/(20\,\Omega)+(1)/(20\,\Omega)+(1)/(20\,\Omega) )`

`R_(eq,1) = (1)/((4)/(20\,\Omega) )`

`R_(eq,1) = 5\,\Omega`

2nd Stage (1 resistor in series)

`R_(5) = 20\,\Omega`

Now, the equivalent resistance is:

`R_(eq,2) = R_(eq,1) + R_(5)`

`R_(eq,2) = 5\,\Omega + 20\,\Omega`

`R_(eq,2) = 25\,\Omega`