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

Answer:

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

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)

$R_{eq,1} = \frac{1}{\frac{1}{R_{1}}+\frac{1}{R_{2} }+\frac{1}{R_{3}}+\frac{1}{R_{4}}}$

If $R_{1} = R_{2} = R_{3} = R_{4} = 20\,\Omega$, then:

$R_{eq,1} = \frac{1}{\frac{1}{20\,\Omega}+\frac{1}{20\,\Omega}+\frac{1}{20\,\Omega}+\frac{1}{20\,\Omega} }$

$R_{eq,1} = \frac{1}{\frac{4}{20\,\Omega} }$

$R_{eq,1} = 5\,\Omega$

2nd Stage (1 resistor in series)

$R_{5} = 20\,\Omega$

Now, the equivalent resistance is:

$R_{eq,2} = R_{eq,1} + R_{5}$

$R_{eq,2} = 5\,\Omega + 20\,\Omega$

$R_{eq,2} = 25\,\Omega$