Question

Two identical resistors are first connected in series and then in parallel.Find the ratio of equivalent resistances in two cases.

Answer 1

Let one of the resistor be R

Eqv. resistance of the resistor connected in series Rs = 2R

Eqv. resistance of the resistor connected in parallel

1/ Rp = 1/R + 1/R

=> Rp = ½R

1.)  Ratio of eqv. resistance in both the case is

Rs/Rp = 2R/ (R/2)

  = 4:1

Answer 2

let the resistances be R

In Series:

total resistance R1 = R+R
                               = 2R

therefore equivalent resistance of series = 2R


In Parallel:

toal resistance R2 = (R*R) / (R+R)
                              = R² / 2R
 
 therefore equivalent resistance of parallel = R² / 2R

Ratio of their Equvalent Resistance =2R/ (R² / 2R)
                                                         = 4 R² /R²
                                                        = 4 : 1