Question

Prove that Rs /Rp = n square. For n =equal resistance connected on series and parallel

Answer 1

for n equal resistors connected in series

Rs= R+R+R+R+R...........n times = nR

for n equal resistors connected in parallel

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

=> Rp= R/n

=>Rs / Rp = nR / (R/n) = nR × (n/R) = n²

hope this will help you

Answer 2

Answer:

for n equal resistor connected in series, so Rs=R+R+R+R....... n times =nR

for n equal resistor connected in parallel, so 1/Rp=1/R+1/R+1/R.....n times

=====> Rp=R/n

Rs/Rp=nR/(R/n)

nR×n/R=n^2

so,Rs/Rp=n^2