Equivalent resistance in a complex circuit

In summary, the circuit shown has resistors R1 = 0.810 Ω, R2 = 8.10 Ω, R3 = 81.0 Ω, and R0 = 810 Ω. When a 7.70 V power supply is connected between points A and C, the equivalent resistance of the circuit can be calculated using the series and parallel equations. The current through R0 and R1 can then be found by applying the equations for parallel resistors. The branch labeled D can be treated as an open circuit, making it irrelevant to the calculations. Ultimately, the current through R1 can be calculated by dividing the voltage change of 7.7 V by R1.
  • #1
PhysicsMan999
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0

Homework Statement



  1. In the circuit shown, R1 = 0.810 Ω, R2 = 8.10 Ω, R3 = 81.0 Ω, and R0 = 810 Ω.
    See attachment

  1. Calculate the equivalent resistance of the circuit when a 7.70 V power supply is connected between points A and C.
    Calculate the current through R0 and R1

Homework Equations


Series: resistances sum
Parallel: 1/Req=1/R1+1/R2...

The Attempt at a Solution


Okay so I'm not really understanding circuits well. From what I would gather R3 and R0 would be in series, but I'm just really confused about R1 and R2. And I'm not even 100% sure if R3 and R0 are actually in series since it branches off to D between them as well..
 

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  • #2
You're correct that R3 and R0 are in series. Now combine them and notice what happens with the circuit.

Now, why doesn't it matter that D is in between them? Because in this particular scenario, the D branch is an open circuit, so there will be no current flow in it, so you can treat the circuit as if thst branch isn't even there.

So if the B branch is also an open circuit, then...
 
  • #3
I think you should redraw the circuit, leaving off what is irrelevant, including a piece of wire going nowhere and labelled D. Then see what you have.
 
  • #4
Thank you guys! I found R0 and R3 are in series with each other, and so are R1 and R2, and these two series are in parallel with each other. I managed to calculate Req, and the current through R0, but now I'm having trouble calculating the current through R1..I now that parallel resistors are supposed to have the same change in voltage across resistors, but I'm not really sure how to apply that here. I thought that the voltage change would be 7.7, and just divided that by R1 for the current, but that was wrong.
 
  • #5
Figured it out guys! Thanks for the help! Couldn't find an edit button so sorry for the double post just didn't want to unnecessarily take up more of anyones time than needed.
 

Related to Equivalent resistance in a complex circuit

1. What is equivalent resistance in a complex circuit?

Equivalent resistance in a complex circuit refers to the single resistance value that can replace all the individual resistances in the circuit without changing the total current or voltage. It is a way to simplify a complicated circuit into a more manageable form.

2. How is equivalent resistance calculated?

Equivalent resistance can be calculated using Ohm's law, which states that the total resistance in a series circuit is equal to the sum of all the individual resistances, or the reciprocal of the sum of the reciprocals of the individual resistances in a parallel circuit.

3. Why is it important to know the equivalent resistance in a complex circuit?

Knowing the equivalent resistance allows us to analyze and understand the behavior of a complex circuit. It helps in determining the amount of current and voltage in different parts of the circuit, and in designing and troubleshooting circuits.

4. What factors affect the equivalent resistance in a complex circuit?

The equivalent resistance is affected by the number of resistors, their values, and how they are connected in the circuit. In general, adding resistors in series increases the equivalent resistance, while adding resistors in parallel decreases it.

5. Can the equivalent resistance ever be smaller than the smallest individual resistance in a circuit?

No, the equivalent resistance can never be smaller than the smallest individual resistance in a circuit. This is because resistors in parallel offer an easier path for current to flow, so the total resistance is always less than the smallest individual resistance.

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