Physics Olympiad question Electric circuit

[Hashiramasenju]

Homework Statement

In the Circuit(pic attached) the following resistor combination is found.
All the resistrs in the figure has resistance R ohms.
What is the total resistance across AB?

Homework Equations

V=IR
3. The attempt at a Solution
between point A and B there is only one resistor so i thought the answer is R

 

[gneill]

Homework Statement

In the Circuit(pic attached) the following resistor combination is found.
All the resistrs in the figure has resistance R ohms.
What is the total resistance across AB?

Homework Equations

V=IR
3. The attempt at a Solution
between point A and B there is only one resistor so i thought the answer is R

No, there are multiple paths that current could take from A to B. Look for opportunities to combine series and parallel resistances to reduce the circuit complexity.

Your Relevant Equations should have included the formulas for combining resistances.

 

[Hashiramasenju]

No, there are multiple paths that current could take from A to B. Look for opportunities to combine series and parallel resistances to reduce the circuit complexity.

Your Relevant Equations should have included the formulas for combining resistances.

I could do the part i) I am stuck with the part ii)

 

[gneill]

Show your work for part (i) and what you've tried for part (ii).

 

[Hashiramasenju]

This is for part i)
But for part ii) i seriously had no idea.

 

[gneill]

Part i) work is good.

For part ii), can you not spot any series or parallel connections? What type of connection relationship do resistors AD and DC have?

 

[Hashiramasenju]

yeah i noticed that resistors ad and dc are in series. Then resistors ac is parallel with ad&dc. so the only resistor left out is bc

 

[gneill]

yeah i noticed that resistors ad and dc are in series. Then resistors ac is parallel with ad&dc. so the only resistor left out is bc

Yes, so can you reduce the whole network down to a single resistance?

 

[Hashiramasenju]

no. I really have no idea how to include resistance ab and bc in the circuit

 

[gneill]

You've already identified that AD is in series with DC and so can be replaced by a single resistor, say "ADC". You also pointed out that this ADC is in parallel with AC, so that pair in turn can be replaced with a single resistor. What's the value of that resistor?

Redraw the circuit with that new resistor in place and the remaining resistors.

 

[Hashiramasenju]

I think i got it 5R/8
Thank you !

 

[gneill]

I think i got it 5R/8
Thank you !

Looks good.

You're welcome