What is the minimum number of 10-ohm, one-ampere resistors needed to achieve an equivalent resistance of 10 ohms capable of carrying a two-ampere load?

To achieve an equivalent resistance of 10 ohms while also being able to carry a two-ampere load, it’s essential to consider how resistors can be arranged in series and parallel configurations.

Each of the resistors has a resistance of 10 ohms and can carry a load of 1 amp. If these resistors are connected in parallel, the formula for calculating equivalent resistance is given by:

[

\frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \ldots

]

For resistors in parallel, the equivalent resistance decreases. If we want the total resistance to stay at 10 ohms with a two-ampere load, we must consider that we need to use enough resistors to handle that current safely without exceeding the limit of each individual resistor.

Using four 10-ohm resistors in parallel can be calculated as follows:

[

R_{\text{eq}} = \frac{10, \Omega}{n}

]

where n is the number of resistors. Setting the equivalent resistance to 10 ohms:

[

10,