Solve Circuit Problem: 2 Ways to Wire 450 Ohm Resistors for 300 Ohms

[Nivlac2425]

Homework Statement

You have a number of identical 450 ohm resistors. There are two ways in which six of these resistors can be wired to give an equivalent resistance of 300 ohms. What are they?

Homework Equations

The Attempt at a Solution

This problem only deals with simple series and parallel circuits.

Is there a way to figure this problem out without trial-and-error drawing out the circuits?
Drawing out and testing the circuits would take too long; mathematically doing it would be easier. But in what way can that be done?

Thanks everyone for helping out!

 

[yoniwei]

Rt = 1/R (x) + R (6-x) let x represent the number of 450 ohm resistors connected in parallel and let y represent the number of resistors connected in series.

should be simple enough algebra?

 

[nlightner]

There are actually several ways to mathematically solve this circuit problem. One approach is to use the equivalent resistance formula for resistors connected in parallel:

1/Req = 1/R1 + 1/R2 + 1/R3 + ...

Where Req is the equivalent resistance and R1, R2, R3, etc. are the individual resistances.

Using this formula, we can set up equations to find the values of resistors that would give us an equivalent resistance of 300 ohms. For example, for two resistors in parallel, the equation would be:

1/300 = 1/R1 + 1/R2

We can then solve for R2 in terms of R1 and substitute that into the equation for three resistors in parallel:

1/300 = 1/R1 + 1/(R1+ R2)

Solving this equation will give us the values for R1 and R2 that would give us an equivalent resistance of 300 ohms. We can repeat this process for six resistors in parallel to find the two different ways to wire them for an equivalent resistance of 300 ohms.

Another approach is to use Kirchhoff's laws, specifically the junction rule and the loop rule, to set up a system of equations and solve for the unknown resistances. This method may be more time-consuming, but it is a more comprehensive approach that can be used for more complex circuit problems as well.

In summary, while drawing and testing the circuits may be a more visual and intuitive approach, using mathematical formulas and principles can also effectively solve this circuit problem.