Find the Equivalent Resistance of a Network

[jumbogala]

Homework Statement

A network consists of a combination of parallel and series connections. What is the equivalent resistance of the network? (Hint: Use the series and parallel resistance formulas).

The network looks like this:

Homework Equations

When a circuit is in series, R = R1 + R2 + R3...

When a circuit is in parallel, R = 1/R1 + 1/R2 + 1/R3...

The Attempt at a Solution

First, c and b are in series, so I just add them up. 5 + 3 = 8.

Now, a, d, and this new resistor of value 8 are in series. So add them up again.
8 + 4 + 1 = 13.

Did I do that correctly?

 

[LowlyPion]

Sorry. B and C are ||.

Not in series.

 

[jumbogala]

They look like they're in series to me... how can you tell?

That changes my answer to 1/5 + 1/3 = 0.533. And 1/0.533 = 1.875.

Then 1.875 + 4 + 1 = 6.875

 

[LowlyPion]

They look like they're in series to me... how can you tell?

That changes my answer to 1/5 + 1/3 = 0.533. And 1/0.533 = 1.875.

Then 1.875 + 4 + 1 = 6.875

That looks more like it.

 

[mplayer]

When a circuit is in parallel, R = 1/R1 + 1/R2 + 1/R3...

This is wrong. I think you meant to write:
1/R_eq = 1/R₁ + 1/R₂ + 1/R₃...

They look like they're in series to me... how can you tell?

Notice that the upper terminals of C and B share a common node. Similarly, the bottom terminals of C and B share a common node.

 

[jumbogala]

Yeah, I meant to write 1/Req = 1/R1 + 1/R2...

So a is in series with c because it only shares one common node? And b and c are in parallel because they share two nodes?

 

[mplayer]

So a is in series with c because it only shares one common node? And b and c are in parallel because they share two nodes?

Well, a better way to say it is this: A is in series with the combination C||B.

If the same current flows through two resistive elements, the elements are in series.
If the same voltage potential is across two elements, the elements are in parallel.

Does that help?

 

[jumbogala]

That helps a lot - I understand now. Thank you!