# Equivalent resistance between points a and b

• zetologos
In summary, the conversation is about a physics problem involving finding the equivalent resistances for parallel and series circuits. The first question asks about the current flow through each resistor when a current is injected at point A and leaves at point B. The second question asks about the equivalent resistance between two points after adding and removing certain resistors. The conversation also includes hints and tips for approaching the problem.
zetologos

## Homework Statement

I don't know where to start. Can anyone recommend a book the instructor didn't assign one.

I don't think a book is necessary, as long as you know how to find the equivalent resistances for parallel and series circuits. For the first question, imagine a current I entering at A and leaving through B. How much current will flow through each of the resistors? You can use this to figure out the voltage drop between the two points.

For the second question, suppose I take off the 3 resistors at the very right. What would the equivalent resistance be between the top-right point and the bottom-right point? You can use this to set up an equation to solve for the equivalent resistance.

Welcome to PhysicsForums!

These are more math / problem solving-type questions, rather than straightforward circuit analysis.

Here's a hint for a: consider what happens when you inject a test current 'I_o' into point A, and figure out how the current flows. Then figure out the voltage at each point (V=IR)

For b, consider that you're adding three series resistors in parallel with a single one. And then you're adding another three series resistors in parallel with the one resistor that you just added previously. Consider: you're far down the line, does adding another three resistors change the equivalent resistance by very much? You should end up solving a quadratic equation using this approach.

Good luck!

EDIT: Obviously, adding three resistors at that point changes the resistance at that point. It shouldn't change the resistance very much at the beginning of your resistor chain.

The second diagram looks too easy if Points A and B on the circuit are the far right top and bottom "corners" on the circuit. There is only one resistor between points A and B? What am I missing?

pgardn said:
The second diagram looks too easy if Points A and B on the circuit are the far right top and bottom "corners" on the circuit. There is only one resistor between points A and B? What am I missing?

All the other paths from A to B that pass through all the other resistors

The first one is done by joining together (with wires) points on the cube that must have the same voltage on them, by symmetry.

If they have the same voltage, no current will flow in the new wires, but they make the problem a lot easier. You get a few sets of parallel resistors in series.

## What is equivalent resistance?

Equivalent resistance is the total resistance of a circuit when all resistors are replaced by a single resistor. It is the resistance that would produce the same current in the circuit as the original combination of resistors.

## How is equivalent resistance calculated?

Equivalent resistance can be calculated using the formula Req = R1 + R2 + ... + Rn, where R1, R2, ... , Rn are the individual resistances in the circuit. For resistors in parallel, the formula is 1/Req = 1/R1 + 1/R2 + ... + 1/Rn.

## Why is equivalent resistance important?

Equivalent resistance is important because it helps us simplify complex circuits and analyze them more easily. It also allows us to determine the total resistance in a circuit, which is necessary for calculating the total current and voltage.

## What factors affect equivalent resistance?

The main factors that affect equivalent resistance are the number and arrangement of resistors in a circuit. Resistors in series add up to a larger equivalent resistance, while resistors in parallel result in a smaller equivalent resistance.

## Can equivalent resistance ever be lower than the smallest individual resistor?

Yes, equivalent resistance can be lower than the smallest individual resistor in a circuit. This happens when resistors are connected in parallel, as the total resistance decreases as more resistors are added in parallel.

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