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

• Nivlac2425
In summary, the problem involves finding two ways to wire six identical 450 ohm resistors to give an equivalent resistance of 300 ohms. This can be solved using the equation Rt = 1/R(x) + R(6-x) where x represents the number of resistors connected in parallel and y represents the number of resistors connected in series. This can be solved algebraically to find the two possible solutions without having to draw out and test circuits.
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?

## 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!

Last edited:
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?

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.

## What is the purpose of solving a circuit problem?

Solving a circuit problem allows us to determine the most efficient and effective way to wire components in order to achieve a desired resistance or current flow.

## What is the difference between series and parallel circuits?

In a series circuit, components are connected in a single path, meaning the total resistance is equal to the sum of each individual resistance. In a parallel circuit, components are connected in multiple paths, meaning the total resistance is less than the smallest individual resistance.

## How do you wire 450 ohm resistors to achieve a total resistance of 300 ohms?

One way to wire the resistors would be to connect them in series, meaning the resistors are connected end to end with no branches. In this case, the total resistance would be 900 ohms (450 + 450). To achieve a total resistance of 300 ohms, a third 450 ohm resistor would need to be added in parallel to the existing series circuit.

## What is the benefit of using parallel wiring for resistors?

Parallel wiring allows for a lower overall resistance, meaning more current can flow through the circuit. This can be beneficial for high-powered circuits or circuits with multiple components.

## Can you mix series and parallel wiring for resistors?

Yes, it is possible to mix series and parallel wiring for resistors in order to achieve a specific resistance. This requires careful calculation and understanding of the circuit components and their individual resistances.

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