Find equivalent resistance in this circuit

In summary: Then, replace that ratio in the original equation and you'll have your answer.In summary, the equivalent resistance Rab between nodes A and B can be found by setting up KCL and KVL equations and solving for the ratio Vab/Iab in terms of the resistors. This ratio can then be substituted into the original equation to find the value of Rab.
  • #1
Hyperfluxe
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0

Homework Statement


http://session.masteringengineering.com/problemAsset/1515645/4/Steif.ch02.p28.jpg
Find the equivalent resistance between node A and B, knowing that Rab = Vab/Iab

Homework Equations


KCL and KVL, I know.


The Attempt at a Solution


There is nothing in series or parallel here, so what I did is set up KCL equations and KVL loop equations (top and bottom loops), so 6 equations with 6 unknowns and I can find Iab. I don't know how to find Vab though...
 
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  • #2
You don't find Vab, you stick a voltage source there (value of your choosing, or just leave it as a variable, "Vab"). The equivalent resistance Rab is given by the ratio Vab/Iab.

Presumably the Vab variable will cancel out in the workings leaving you with an expression for Rab in terms of R alone.
 
  • #3
I'm still confused though, is my method of finding Iab correct?
 
  • #4
Hyperfluxe said:
I'm still confused though, is my method of finding Iab correct?

Well, the approach of finding Iab given a source voltage Vab is correct. But you haven't shown the details of your work so it's not possible to say more.
 
  • #5
Hyperfluxe said:
I'm still confused though, is my method of finding Iab correct?

You don't need to solve the equations to find Iab or Vab their own.

Rab = Vab/Iab

so reaarange the equations until you get one for the ratio Vab/Iab in terms of the resistors only.
 

FAQ: Find equivalent resistance in this circuit

How do I calculate the equivalent resistance in a circuit?

To calculate the equivalent resistance in a circuit, you can use Ohm's Law (R = V/I) or the series and parallel resistance equations depending on the configuration of the circuit. You will need to know the voltage and current values for each component in the circuit.

What is the purpose of finding the equivalent resistance in a circuit?

Finding the equivalent resistance in a circuit is important because it allows you to simplify a complex circuit into a single resistor, making it easier to analyze and understand the behavior of the circuit. It also helps in determining the total current and voltage in the circuit.

Can the equivalent resistance in a circuit be less than the smallest individual resistor?

No, the equivalent resistance in a circuit can never be less than the smallest individual resistor. It can only be equal to or greater than the smallest resistor. This is because adding more resistors in parallel will decrease the overall resistance, but adding more resistors in series will increase the overall resistance.

How does the equivalent resistance change when resistors are connected in series or parallel?

When resistors are connected in series, the equivalent resistance increases since the current has to pass through each resistor in succession, resulting in a higher overall resistance. When resistors are connected in parallel, the equivalent resistance decreases since the current can flow through each resistor separately, resulting in a lower overall resistance.

Can the equivalent resistance in a circuit be negative?

No, the equivalent resistance in a circuit cannot be negative. Resistance is a physical property that represents the opposition to the flow of electric current. Negative resistance would mean that the current increases with increasing voltage, which goes against Ohm's Law and is not physically possible.

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