Question

two identical resistors of 7ohm are each connected to a battery of 6v. calculate the ratio of the powers consumed by the resulting combinations with minimum resistance and maximum resistance.

Answer 1

1)in series
10 + 10 = 20Ω
now find the current
I=V/R
 =6/20
 =.3A
now power
P1=V(I)
   =6×.3
  = 1.8W
2)in parallel
1/R=1/R+1/R
  =1/10+1/10
R  =5Ω
now current
I=V/R
 =6/5
 =1.2A
power
P2=V×I
  =6×1.2
  =7.2W

Ratio
P1/P2=1.8/7.2
          =.25W

Answer 2

With minimum resistance the resistors will be connected in parallel.

For minimum resistance:

1/Rt = 1/R1 + 1/R2

Rt = effective resistance

R1 = R2 = 7 ohms

Doing the substitution we have :

1/Rt = 1/7 + 1/7

= 2/7

Rt = 7/2 = 3.5 ohms

At maximum resistance the resistors are connected in series:

Rt = R1 + R2

= 7 + 7 = 14 ohms.

The formula for power is given as :

Power = V²/R

Power at Minimum resistance is given by:

P1 = 6²/3.5 = 10.29 watts

Power at maximum resistance :

P2 = 6²/14

= 36/14 = 2.57 watts

P1 : P2 is given by :

36/3.5 × 14/36

= 4/1

= 4 : 1