Question

n identical resistors each of resistance r when connected in parallel, have a total resistance R. When these resistors are connected in series, then effective resistance in terms of R is:​

Answer 1

Answer:

more resistance is required for series'

Explanation:

if you want to decrease resistance younhave to use parrell

Answer 2

Resistance of each resistor = r

Net Resistance of the parallel combination = R

But, In parallel combination net resistance (Req) is given by:

1/Req = 1/R1 + 1/R2 + 1/R3 + ........ + 1/Rn

And, Req = R ............. (according to ques)

=> 1/R = 1/r + 1/r + 1/r + .......... up to n times

1/R = (1+1+1+1..... up to n times)/r

1/R = n/r

R = r/n

r = nR

=> Each resistance of magnitude r is nR.

Now, when these resistances are connected in series then their net resistance becomes:

R(net) = R1 + R2 + R3 .......

R(net) = r + r + r + r ........ up to n times

R(net) = nr

But r = nR,

=> R(net) = n(nR)

= Rn^2

Hence, in series combination the effective resistance would be:

R(net) = (n^2)R.