Simplifying a resistance circuit

In summary, the conversation was about finding the Thevein resistance of a circuit and the confusion around identifying parallel connections between resistors. The expert summarizer provided a step-by-step explanation of how to identify parallel connections and calculate the total resistance of the circuit, ultimately determining the total resistance to be 8.5 Ohms. The conversation ended with gratitude from the person seeking help.
  • #1
GBA13
73
0

Homework Statement


Hi guys,

I am trying to find the Thevein resistance of a circuit, I'm only stuck on finding Rth. Can you help?

I have included a screen shot.

Homework Equations

The Attempt at a Solution


Well I thought that I could combine the two bottom 1 ohms in series, the 4 and 12 in parallel and then combine the three remaining for a total of 10 ohms. But I am starting to think that the two 1 ohm resistors don't actually share the same to nodes so I am now a bit stuck! Any help would be greatly appreciated.
 

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  • #2
GBA13 said:

Homework Statement


Hi guys,

I am trying to find the Thevein resistance of a circuit, I'm only stuck on finding Rth. Can you help?

I have included a screen shot.

Homework Equations

The Attempt at a Solution


Well I thought that I could combine the two bottom 1 ohms in series, the 4 and 12 in parallel and then combine the three remaining for a total of 10 ohms. But I am starting to think that the two 1 ohm resistors don't actually share the same to nodes so I am now a bit stuck! Any help would be greatly appreciated.
The two 1 Ohm resistors do indeed share the same nodes; That makes them parallel connected, not serial.
 
  • #3
Opps.. my mistake! I'm a little bit confused though, I can see that the two 1ohm obviously share the same bottom node, but I'm not really sure how the top ones are the same, I see they are connected by a wire but as the nodes are also connected to other resistors I thought they wouldn't be in parallel..

So then that makes then that means that their combined resistance is 1 ohm. So then the 4 and 12 are is parallel for a resistance of 3 ohms, making the total resistance 9 ohms?

Thanks for the help!
 
  • #4
GBA13 said:
Opps.. my mistake! I'm a little bit confused though, I can see that the two 1ohm obviously share the same bottom node, but I'm not really sure how the top ones are the same, I see they are connected by a wire but as the nodes are also connected to other resistors I thought they wouldn't be in parallel..
As long as two components share two nodes they are parallel-connected regardless of what other components may also connect to those nodes. It's series connections that are finicky that way -- components that are in series must be the "sole proprietors" of the node that they share.
So then that makes then that means that their combined resistance is 1 ohm. So then the 4 and 12 are is parallel for a resistance of 3 ohms, making the total resistance 9 ohms?
Ah, so close. Two 1 Ohm resistors in parallel is how many Ohms?
 
  • #5
Oh thanks! makes much more sense!

Once again, Opps! 1/1 + 1/1 = 2 so its 1/2. So the total resistance is 8.5 Ohms! :)
 
  • #6
GBA13 said:
Oh thanks! makes much more sense!

Once again, Opps! 1/1 + 1/1 = 2 so its 1/2. So the total resistance is 8.5 Ohms! :)
Ta da! Yup. :smile:
 
  • #7
Yay! Thanks very much, you've been really helpful! :)
 

What is a resistance circuit?

A resistance circuit is a circuit that contains at least one resistor, which is a passive component that resists the flow of electrical current. It is used to control the amount of current flowing through a circuit and plays a crucial role in regulating the flow of electricity in electronic devices.

Why is it important to simplify a resistance circuit?

Simplifying a resistance circuit can help in analyzing and understanding the circuit's behavior more easily. It can also help in identifying the key components and their relationship with each other, making it easier to troubleshoot any issues that may arise.

What are the steps for simplifying a resistance circuit?

The steps for simplifying a resistance circuit are as follows:

  • Identify all the resistors in the circuit.
  • Combine resistors that are in series by adding their resistances.
  • Combine resistors that are in parallel by using the formula 1/R(total) = 1/R1 + 1/R2 + ... + 1/Rn.
  • Repeat the previous step until all resistors are simplified into one equivalent resistor.

What is an equivalent resistor?

An equivalent resistor is a single resistor that has the same resistance as a combination of multiple resistors in a circuit. It simplifies the circuit and makes it easier to analyze and understand.

What are some common mistakes to avoid when simplifying a resistance circuit?

Some common mistakes to avoid when simplifying a resistance circuit are:

  • Forgetting to include all resistors in the circuit.
  • Incorrectly combining resistors in series or parallel.
  • Not using the correct formula for calculating the equivalent resistance.
  • Forgetting to convert resistors in parallel to series or vice versa before combining them.

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