Resistance of rings

Extend the ray A towards B to make the line pass through the centre of circles and finally reach B take this the line of symmetry now on the part of it we have half the length of our original wire and the other half below it. So as $R$ is proportional to length so the resistance of upper wire is $R/2$ and the lower wire is also $R/2$ and they are in parallel so the answer yields $R/4$ .

$a=1$ $b=4$

The answer is $\boxed{5}$

The arrangement is irrelevant, as they are all in series. Resistance is equal to ρl/A, so the hoop of radius 6 has a total resistance of 6R/21 when in a straight line, the hoop of radius 5 is 5R/21, etc. When bent into a hoop, each half has half the resistance of the straight wire, and the two halves are in parallel, leading to Rhoop=Rstraight/4. Summing 6R/21 + 5R/21 ... 1R/21 yields 1R, which can then be divided by 4 to yield the total resistance of R/4. 1 + 4 = 5

A resistance folded into two in parallel is always (1/2)(1/2) for half length and also half resistance regardless of whether the parallel lines are touching each other side by side provided the connections are perfect. Therefore the resistance is $\frac14$ R.

Answer: 5

Let the radius be r, 2r, 3r, 4r, 5r, 6r. 2πr( 1 + 2 + 3 + 4 + 5 + 6) = L 42πr = L r = L/42π 2πr = L/21

.: The resistances are R/21, 2R/21, 3R/21, 4R/21, 5R,21, 6R/21. Each half of the loop has resistance R/42, 2R/42..... till 6R/42 respectively. Since the two halves will be in paralley, the resistances further get halved into R/84, 2R/84,.......till 6R/82. Now, these resistances are in series. Net R = Summation of these resistances. = R(1+2+3+4+5+6)/84 = 21R/84 = R/4 Comparing we can see that a = 1, b =4. .: a + b = 5

let the radius be r , 2r ,3r , 4r , 5r , 6r Length = x.r =x 42 pi the rest can be calculated using this n=information . the answer will be 5

Upper half is similar to lower half so each half can be represented as R/2

R/2 // R/2= R/4

42πr=l Resistance=R=(rho)l/A i.e. R is directly proportional to l Hence l can be converted in terms of R.

Each hoop is equivalent to parallel circuits in series With other parallel circuits. Hence R(equivalent)=R/4 a=1 b=4 a+b=5