Conceptual Question about Equivalent Resistance

[jumbogala]

Homework Statement

I don't quite understand how to read circuit diagrams, so I'm not sure how to find the equivalent resistance in some cases.

What is the equivalent resistance of circuits A and B?

I drew a picture to help me explain what I'm talking about:

Homework Equations

The Attempt at a Solution

I know circuit B is definitely in parallel, so the equivalent resistance is 1/R = 1/R1 + 1/R2.

But is circuit A in parallel, too? I think it is but I'm not 100 % sure.

 

[Shooting Star]

What is the equivalent resistance of circuits A and B?

I drew a picture to help me explain what I'm talking about:

Homework Equations

The Attempt at a Solution

I know circuit B is definitely in parallel, so the equivalent resistance is 1/R = 1/R1 + 1/R2.

But is circuit A in parallel, too? I think it is but I'm not 100 % sure.

You are correct -- the two circuits are absolutely equivalent. It does not matter how you draw the resistance R2 as long as it is there somewhere between the two points where the wires from R2 join the wire containing R1.

"Parallel" does not mean that the resistances have to be literally parallel.

 

[nlightner]

Hello! It's great that you're trying to understand circuit diagrams and equivalent resistance. Let me explain a bit more about how to read circuit diagrams and how to find the equivalent resistance in different cases.

First, let's talk about circuit diagrams. They are a visual representation of a circuit, showing the connections between the different components. The lines connecting the components represent wires, and the symbols represent different elements such as resistors, batteries, and switches.

Now, to find the equivalent resistance of a circuit, you need to understand how the components are connected. In circuit A, the resistors are in series, meaning they are connected one after the other in a single path. In this case, the equivalent resistance is simply the sum of all the resistors. So the equivalent resistance of circuit A is R1 + R2 + R3.

In circuit B, the resistors are in parallel, meaning they are connected at both ends. In this case, the equivalent resistance is calculated using the formula you mentioned, 1/R = 1/R1 + 1/R2. So the equivalent resistance of circuit B is 1/R = 1/R1 + 1/R2 + 1/R3.

I hope this helps you understand how to find the equivalent resistance in different circuits. Remember, it's important to first understand how the components are connected in order to correctly calculate the equivalent resistance. Keep practicing and you'll get the hang of it!