Question

Two identical resistors each of resistance 2 ohm are connected in turn (1) in series (2)in parallelto a battery of 12V calculate the ratio of power consumed in two cases

Answer 1

(1) IN SERIES

Total Resistance in Series = R₁ + R₂
                                          = 2 + 2
                                          = 4 Ohm
Potential Difference(V) = 12V
Current(I)= V/R
               =12/4
               =3Ampere
Power = VI
           = 12*3
           =36 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)= 12Volts
Current(I)= V/R
               = 12 Ampere
Power= VI
          = 12*12
          = 144 Watt

Power in series : Power in Parallel
36 : 144
1 : 4

Answer 2

Answer:

When the two resistors are in series, total resistance =Rs=10+10=20Ω

Is=V/R=6/20=0.3A

When the two resistors are connected in parallel, total reresistances:

1/Rp=1/10+1/10

Rp=5ohm

1p=6/5=1.2A

Power = V I

Thus, the ratio of power consumed in series and parallel combination is;

Power=VI

Ps/Pp=0.3/1.2=0.25W