Question

Two identical resistors each of resistance 12 ohm are connected 1) in series 2) in parallel, in line to a battery of 6volts. Calculate the ratio of power consumed in the combination of resistors in the two case

Answer 1

for first case r=24
second case r=12
V=6v
p=v sq/r
v is same for both cases
p1/p2=r2/r1
=1/2

Answer 2

(1) IN SERIES

Total Resistance in Series = R₁ + R₂

                                         = 12 + 12

                                         = 24 Ohm

Potential Difference(V) = 6V

Current(I)= V/R

              =6/24

              =1/4 Ampere = 0.25A

Power = VI

          = 6*0.25

          = 1.5 Watts

(2) IN PARALLEL

1/R₁ + 1/R₂ = 1/Rₐ (Where Rₐ is the total resistance)

1/2 + 1/2 = 1/Rₐ                                            

2/2 =1/Rₐ

1/1 = 1/Rₐ      

1 Ohm = Rₐ

Voltage (V)= 6Volts

Current(I)= V/R

              = 6 Ampere

Power= VI

         = 6*6

         = 36 Watt

Power in series : Power in Parallel

1.5 : 36

1 : 24