- #1

VinceS

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## Homework Statement

Using the known values of R1, R2, R3, R4, R5, R6, and a 5.03kΩ resistor, find the resistance between nodes 1 and 3 in Circuit 1 and Circuit 2.

Circuit 1 is a T-network composed of R1(1.0935kΩ), R2(1.06kΩ), and R3(1.07). Node 2 is connected directly to R2 and Node 3 is connected directly to R3 - the goal is calculate the resistance between nodes 1 and 3 when a 5.11kΩ resistor is connected between them(R5.1)

Circuit 2 is a PI-network composed of R4(2.980kΩ), R5(2.980kΩ), and R6(2.87κΩ). Node 1 is connected directly R4 and R6 while Node 2 is connected to R4 and R5. Node 3 is connected R5 and R6. The goal is the same as above - calculate the resistance between Nodes 1 and 3 when there is nothing connecting Nodes 2 and 3 and then with a 5.1κΩ resistor between them.

## Homework Equations

I'll try to model the diagram for a better understanding, don't really have access to a scanner at the moment.

Circuit 1

N1 -----R1(1.0935kΩ) ------R2(1.06kΩ)-----N2

.......|......

........R3(1.07κΩ).....R(5.03) should be here, connected between N2 and N3

.......|......

........N3......

Circuit 2

N1------------R4(2.98κΩ)---------------N2

...|......|...

...|......|...

...R6(2.87κΩ)....R5(2.98κΩ)...R(5.03) would be in parallel with this resistor.

...|--------------------------|...

.......|......

.......N3.....

## The Attempt at a Solution

I actually already know the values are supposed to be 2.01kΩ for Circuit 1 and 1.85κΩ and 1.99κΩ for Circuit 2 as this was a lab and I actually measured the values using a breadboard circuit and a multimeter. However, for analysis I'm intended to calculate the expected values, and for the life of me I can't figure out how to approach this.

The first thing I tried for Circuit 1 was to add R2 and R3 as series resistors, then combine them in parallel with R(5.03) which gave an equivalence resistance of~1.5kΩ. Then I combined that in parallel with R1, but that gave me about .67kΩ, which isn't even close to what I measured.

After that, I tried adding just R5.03 in parallel with (R1+R2), and that gave me 1.51kΩ - again considerably less than something around 2.01kΩ.

Is there something I'm missing here? Should I be using γ-Δ transformations, or would that just make a bigger mess of things?

If anyone can help steer me to a more accurate method of calculation, I would really appreciate it.

Also, I apologize if there was something in the formatting I got wrong - First time I've ever used this forum!