Question

if a wire of resistance R is cut into n equal parts all parts are first connected in series and then in parallel calculate ratio of series and parallel combination of resistors.​

Answer 1

If a wire of resistance R is connected into n equal parts

the resistance of each part will be equal to

R/n

hence

R1 = R2 = R 3 =R 4 .. .Rn = R/ n

CASE 1 :

All these resistors are connected in parallel

So the resultant resistance

1/Rp = 1/R1 +1/R2 + 1/R 3 +1/R 4 ....1/Rn

1/Rp = n /R +n/R + n/R +n/R ....n/R

As n/R resistors are connected n times in parallel

1/Rp = (n/R)n

Rp = R/n²

CASE 2:

Now these resistors are connected in series

Rs = R1 + R2 +R 3 +R 4 ...Rn

As resistance of each part is R/n

Rs = R/n +R/n +R/n + R/n .....n R/n

As R/n resistors are connected n times in series

Rs = n (R/n)

Rs = R

RATIO OF SERIES AND PARALLEL COMBINATI ON IF RESISTORS:

Rs /Rp = R×n² / R

Rs /Rp = n²