Modification of Wheatstone Bridge

[songoku]

Homework Statement

This is not homework, the question just crossed my mind when I was reviewing about Wheatstone bridge. Please see the picture below

Relevant Equations

Series and Parallel circuit

I want to ask what the total resistance of the circuit will be if R2 is removed and being replaced with ideal wire.

I think R1 and R3 will be parallel → let this be R6

R6 will be series with R4 → let this be R7

Then R7 will be parallel to R5

Is that correct? Thanks

 

[Charles Link]

I believe you have it correct. :)

 

[Delta2]

I also think you are correct.

 

[songoku]

If both R₁ and R₂ are replaced by ideal wire, would I need to use Delta - star transformation?

Something like this:

where:
$$R_A=\frac{R_3 \times R_4}{R_3+R_4+R_5}$$
$$R_B=\frac{R_3 \times R_5}{R_3+R_4+R_5}$$
$$R_C=\frac{R_4 \times R_5}{R_3+R_4+R_5}$$

After that, $R_A$ will be parallel to $R_B$ and the result will be series with $R_C$

Is that correct? Thanks

 

[Delta2]

No I don't think that's correct , if $R_1$ and $R_2$ are replaced by ideal wires then we shall have $V_D=V_A=V_B$ which means that effectively $R_3$ will also be out of the game. So you ll just have $R_4$ and $R_5$ in parallel. That's what I think.

 

[songoku]

No I don't think that's correct , if $R_1$ and $R_2$ are replaced by ideal wires then we shall have $V_D=V_A=V_B$ which means that effectively $R_3$ will also be out of the game. So you ll just have $R_4$ and $R_5$ in parallel. That's what I think.

Ah I see

Thank you very much for the help and explanation Charles Link and Delta2