Derive expression for equivalent resistance of a parallel combination of resistances. (b) Calculate the ratio of equivalent resistance for a series combination of n number of identical resistors to the parallel combination of the same type of n number of resistors.

Derive expression for equivalent resistance of a parallel combination

1.	Derive expression for equivalent resistance of a parallel combination of resistances. (b) Calculate the ratio of equivalent resistance for a series combination of n number of identical resistors to the parallel combination of the same type of n number of resistors.
Answer» Solution :(b) Let value of each resistor be `R Omega` Then for series COMBINATION of N such RESISTORS, the EQUIVALENT resistance `R_s` is `R_s=R+R+…n time s= nR` If equivalent resistance for PARALLEL combination of these resistors be `R_p` then `1/R_p=1/R+1/R+......n time s=n/R` `implies R_p=R/n` `therefore R_s/R_p=(nR)/(R//n)=n^2`