## richyw 3 years ago Consider a uniform metal ring. Between points A and B a resistance of $$20\Omega$$ is measured. What is the resistance between points A and C?

1. richyw

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2. richyw

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3. richyw

so I set it up like I just drew above. The answer is $$20 \Omega$$ but I can't figure out why, I keep getting $$15\Omega$$. I know from A to B has resistance $$20\Omega$$ so I put$R_{AB}=\frac{2R(R+R)}{2R+(R+R)}=\frac{4R^2}{4R}=R=20\Omega$So this is the value of R right? Then I do the same thing for between A & C and get$R_{AC}=\frac{R(2R+R)}{R+(2R+R)}=\frac{3R^3}{4R}=\frac{3}{4}R=15\Omega$

4. richyw

does anyone see where I am going wrong?

5. akash123

6. akash123

in 2nd expression...3/4 R...why u r putting R=20 ohm?

7. akash123

u have been given...resistance between points A and B is 20 ohm.. but u r using R(Ac) or R(CB)= 20 ohm....which is wrong.

8. akash123

does it help u?

9. Algebraic!

Are the lengths given more precisely?

10. Algebraic!

like A and B are halfway around the circle, and C is 1/4 the way from A?

11. Algebraic!

you there?