Basic Circuits - Equivalent Resistance

[subwaybusker]

Homework Statement

Find the Resistance between terminals B-C, B-D

Homework Equations

The Attempt at a Solution

The book says that the 2 80-ohm resistors are in parallel for terminals A-B, and the answer for B-C=90ohms, B-D=85ohms. I don't quite understand why this is. Is it because the 2 80ohm resistors are in series between terminals B-C and B-D, and therefore it short circuits because the other path (wire only) is 0 ohms? Does this mean that whether the resistors are in series or parallel depends on the path taken?

 

[berkeman]

Correct about the short circuit around the 80 Ohm resistors for the path B-C and B-D.

 

[Mene]

It is correct that the two 80-ohm resistors are in parallel for terminals B-C and B-D. This means that they are connected to the same two points (B and D) and have the same voltage drop across them. This results in a combined resistance of 40 ohms for the two resistors. This can be calculated using the formula 1/R = 1/R1 + 1/R2, where R1 and R2 are the individual resistances.

As for the second part of your question, whether the resistors are in series or parallel depends on the path taken by the current. In this case, the current can travel through both resistors in parallel, so they are considered to be in parallel. However, if the current could only travel through one resistor and then the other, they would be in series.

It is important to note that the equivalent resistance of a circuit does not depend on the path taken by the current. It only depends on the arrangement of the resistors and can be calculated using the appropriate formula.