Question

The resistance of N equal resistors in series is R, then the value of resistance if they are connected in parallel. Plz explain .....

Answer 1

Let resistance of each resistor is r
case 1 :- N resistors are joined in series combination.
so, $R_1+R_2+R_3+R_4+....+R_N=R_{eq}$

or, r + r + r + .... N times = R [as given in question]

=> rN = R

r = R/N ........(1)
hence, resistance of each resistor is R/N

case 2 :- N resistors are joined in parallel combination.
so, $\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+.....+\frac{1}{R_N}=\frac{1}{R_{eq}}$

or, 1/r + 1/r + 1/r +..... N times = 1/Req

N/r = 1/Req

from equation (1),

N/(R/N) =1/Req

Req = R/N²

hence, the value of resistance is R/N² if they are connected in parallel combination.

Answer 2

Answer:

the required resistance is r/x^2

hope it helps you