How to Transform a Circuit to One Resistor?

[builder_user]

Homework Statement

It's only one question. How to transform this ciruit to only one resistor?

Homework Equations

The Attempt at a Solution

 

[phinds]

you haven't said anything about what you know or what you have tried. No one is going to just DO it for you, but I'm sure folks will be happy to help you learn how to do it if you say what you know and what you've tried. "Don't know squat and haven't tried anything" is not likely to get you any help.

 

[builder_user]

what you have tried

that all my ideas for now(where Rx Ry Rz are the results of "triangle->star" transformation)

 

[gneill]

Yes, a Delta-Y transformation will get you there.

Another approach is to imagine a voltage source V across the terminals and solve the loop equations for the current in the voltage source loop. The ratio V/I is the equivalent resistance.

 

[builder_user]

Another approach is to imagine a voltage source V across the terminals and solve the loop equations for the current in the voltage source loop. The ratio V/I is the equivalent resistance.

What does it mean "imagine"?(Not a word)


For this circuit(?) Delta-Y transformation does not help.(Find U1/U2)

 

[gneill]

Imagine: pretend; postulate; suppose

 

[builder_user]

Imagine: pretend; postulate; suppose

I mean in equatations.
Use U or some "image U(E)"?

 

[gneill]

I mean in equatations.
Use U or some "image U(E)"?

I meant to suggest that you imagine that you've connected a voltage source V (or U, or E, or whatever variable name you wish) at the open terminals where you want to find the resistance. If you solve for the current that this voltage produces, then you can find the resistance as V/I.

 

[builder_user]

I meant to suggest that you imagine that you've connected a voltage source V (or U, or E, or whatever variable name you wish) at the open terminals where you want to find the resistance. If you solve for the current that this voltage produces, then you can find the resistance as V/I.

I still don't understand.Sth like this?

 

[gneill]

I still don't understand.Sth like this?

Yes, exactly.

 

[builder_user]

Yes, exactly.

But how can it help?What loop includes E?

 

[gneill]

But how can it help?What loop includes E?

E --> R3 --> R4 --> back to E

 

[builder_user]

E --> R3 --> R4 --> back to E

A!I see now.

What's with 5# scheme?

 

[gneill]

A!I see now.

What's with 5# scheme?

You could use a similar method, solving for the current in the final loop to find the voltage across R5. Once again it's just three loops to be concerned with.

As an alternative, I might be tempted to start from U1 and build Thevenin equivalents, absorbing more and more of the network as I progress across, until I'd be left with one Thevenin voltage and resistance.

 

[gneill]

By the way, in your second circuit, does resistor R3 have a value?

 

[builder_user]

Can I do like that?

When I find I2-I3=I(on R=30 Ohms) will be I=U2/R(30)?

 

[gneill]

Can I do like that?

When I find I2-I3=I(on R=30 Ohms) will be I=U2/R(30)?

What happened to diagonal resistor R4? It should make two loops out of the "square" R3-R2-R5-R6.

You don't want U2 to be in a loop: it's a 'measurement' that you want to make, not a source voltage. It happens to be the voltage across R5.

 

[gneill]

The loops I had in mind are as depicted in the attached figure.

 

[builder_user]

What happened to diagonal resistor R4?.

Delta-y transformation

 

[gneill]

Delta-y transformation

Ah. I see. So now you're down to a situation with just two loops to worry about.

 

[builder_user]

When I find I1 && I2 then I can find I3.I3*R(30)=U2 right?

 

[gneill]

When I find I1 && I2 then I can find I3.I3*R(30)=U2 right?

Since the terminals where U2 is measured are an open circuit, I3 must be zero.

The current through the 30 Ohm resistor (R5) will be determined by your I2.

 

[builder_user]

Since the terminals where U2 is measured are an open circuit, I3 must be zero.

Does it mean that if I have such circuit(pic.) current i through R1 exists but when circuit does not have R1 there is no current i?

 

[gneill]

Does it mean that if I have such circuit(pic.) current i through R1 exists but when circuit does not have R1 there is no current i?

I'm not sure that I follow what you are saying. Is U in this circuit a real voltage source? Can you draw the circuit you have in mind that does not have R1?

 

[builder_user]

I'm not sure that I follow what you are saying. Is U in this circuit a real voltage source? Can you draw the circuit you have in mind that does not have R1?

Here

 

[gneill]

Here

Well, if U is a voltage source, then the current i exists with or without R1. It will of course have different values for the two cases.

 

[builder_user]

It is U like U2(or U1) in previous circuit

 

[gneill]

It is U like U2(or U1) in previous circuit

In the previous circuit you're looking for a relationship between U1 and U2. That means, if you put a real source (say V1) where U1 is, you want to find what the open-terminal voltage is at the terminals U2. In such a case the terminals at U2 are open -- not connected to anything (except perhaps a voltmeter!). So no current will flow through U2.

Alternatively, you could put a real voltage source (say V2) where U2 is, and measure the resulting voltage at the U1 terminals. Again, in such a case the terminals at U1 would be open -- not connected to anything, and no current would flow there.

 

[builder_user]

In the previous circuit you're looking for a relationship between U1 and U2. That means, if you put a real source (say V1) where U1 is, you want to find what the open-terminal voltage is at the terminals U2. In such a case the terminals at U2 are open -- not connected to anything (except perhaps a voltmeter!). So no current will flow through U2.

Alternatively, you could put a real voltage source (say V2) where U2 is, and measure the resulting voltage at the U1 terminals. Again, in such a case the terminals at U1 would be open -- not connected to anything, and no current would flow there.

А!There is no current if I have voltage source in the circuit?

 

[gneill]

А!There is no current if I have voltage source in the circuit?

All I am saying is, if the terminals at U2 are open (not connected to a source), then there is no loop and no current flows (through terminals U2).