Finding the equivalent resistance of this circuit?

[oomba]

Hello

Homework Statement

**attachment of problem diagram at bottom**
1)Find the current through R3
2) Find the total equivalent resistance of the circuit

Homework Equations

Ohm's law, parallel resistances, series resistances, Thevenin's theorem, and all that jazz

The Attempt at a Solution

Okay, for #1, I actually got already. I thought the easiest way to do it would be to utilize Thevenin's equivalent method. So I was able to reduce the circuit down to just the thevenin "load" voltage (which I computed as (7E/15), the thevenin resistance (which I got (22R/15) for, and the load resistor R3. I found the current through R3 to be (7E)/(37R) and I'm pretty sure that's correct.

The real problem is with finding the equivalent resistance of those 5 resistors. I don't see any easily attainable series/parallel resistor combinations thanks to that middle wire with the resistance on it, unless I'm overlooking something pretty badly. Being that there are no numbers given in this problem, what type of approach should I attempt to find Req of that entire branch?

If you can't see the pic, it's basically a closed, looped rectangle located between the terminals of the battery. The rectangle is divided into 2 squares by a wire with a resistance on it, where there are 2 resistors "in a parallel configuration" with each other on both squares.

 

[kamerling]

You can't find the equivalent resistance with replacing series or parallel resistances. you have to compute the current through the whole circuit as a function of V and then if you find that I = (constant) * V, that constant is the equivalent resistance of the whole circuit.

You can do it with Thevenin. I would use any resistor that isn't R_3 for the load, because if you have the current through any other resistance, you can find the potential of one of the nodes, and than other currents in that node with ohms law and kirchhofs current law, and the potential of the other node from that, and the currents through the other node from that.

What I do to solve these is: There's one unknown voltage at every node. Call the potential between R1, R3, and R4: V_1 and the potential between R2, R3 and R5: V_2.
The poles of the battery are at V and 0.
given these unknowns you can calculate all the currents with ohms law
I1 = (V - V1)/R1, I2 = (V-V2)/R2, I3 = (V1 - V2)/R3 etc.
Then use Kirchhofs current law in both nodes to get two equations for the two unknown potentials. After you solve them, you can get the equations above to get all the currents.

 

[Moetasim]

Dear student,

Thank you for your question. Finding the equivalent resistance of a circuit can be a challenging task, but with the right approach, it can be done. First, let's review the basics of resistors in series and parallel.

In a series circuit, the resistors are connected end-to-end, and the total resistance is equal to the sum of individual resistances. In a parallel circuit, the resistors are connected side by side, and the total resistance is given by the reciprocal of the sum of the reciprocals of individual resistances.

In this circuit, we have a combination of series and parallel resistors, with the added complication of a wire with a resistance on it. To find the equivalent resistance of the circuit, we can break it down into smaller parts and apply the appropriate formulas.

Starting with the two resistors in parallel, we can find the equivalent resistance using the formula:

1/Req = 1/R1 + 1/R2

where Req is the equivalent resistance and R1 and R2 are the individual resistances. In this case, R1 and R2 are the two resistors in parallel, so we can substitute their values into the formula and solve for Req.

Next, we can combine this equivalent resistance with the resistor in series, using the formula for resistors in series:

Req = R1 + R2 + R3

where R1 is the equivalent resistance we just found, and R2 and R3 are the remaining series resistors.

Finally, we can add this equivalent resistance to the resistance of the wire, using the formula for resistors in series again:

Req = R1 + R2 + R3 + Rwire

where Rwire is the resistance of the wire.

By following these steps, we can find the equivalent resistance of the entire circuit. I hope this helps, and good luck with your studies. Remember, practice makes perfect when it comes to solving circuit problems!