Question

What is the (a) highest (b) lowest total resistance, that can be secured by combinations of four coils of resistances 2 ohm 10 ohm 14 ohm 6 ohm

Answer 1

Answer:

Ans: Given resistances R1 =4 Ω, R2=8 Ω, R3=12Ω, and R4=24Ω.

(a) If these coils are connected in series, then the equivalent resistance will

be the highest, as R=R1+R2+R3+R4

∴ R=4+8+12+24 = 24Ω

(b) If these coils are connected in parallel, then the equivalent resistance will be the lowest, given by

⇒R=2 Ω

∴ 2 Ω is the lowest total resistance

Answer 2

Given: Combination of four coil of resistances,

            $R_{1}$= 2Ω

            $R_{2}$= 10Ω

            $R_{3}$= 14Ω

             $R_{4}$= 6Ω

To Find:  a) Highest Total Resistance

               b) Lowest Total Resistance

Solution:

a)Highest Total Resistance :-

The highest total resistance can be find by connecting all the four resistances of coil in Series combination as,

                              $R_{equivalent}$= $R_{1}$ + $R_{2}$ + $R_{3}$ + $R_{4}$

Now,

By applying above equation we get,

                          $R_{equivalent}$= $R_{1}$ + $R_{2}$ + $R_{3}$ + $R_{4}$

                         $R_{equivalent}$= 2Ω + 10Ω + 14Ω + 6Ω

                        ∴ $R_{equivalent}$= 32Ω

∴ The Highest Resistance by the combination of the 4 coils = 32Ω

b) Lowest Total Resistance :

The lowest total resistance can be find by connecting all the four resistances of coil in Parallel combination as,

                              $\frac{1}{R_{equivalent}}$= $\frac{1}{R_{1} }$ + $\frac{1}{R_{2} }$ + $\frac{1}{R_{3} }$ + $\frac{1}{R_{4} }$

Now,

By applying above equation we get,

                               $\frac{1}{R_{equivalent}}$= $\frac{1}{R_{1} }$ + $\frac{1}{R_{2} }$ + $\frac{1}{R_{3} }$ + $\frac{1}{R_{4} }$

                           $\frac{1}{R_{equivalent}}$= $\frac{1}{2}$ Ω + $\frac{1}{10}$ Ω + $\frac{1}{14}$ Ω + $\frac{1}{6}$ Ω

                        ∴  $\frac{1}{R_{equivalent}}$ ≈  1.19 Ω

∴ Lowest Total Resistance by the combination of the 4 coils = 1.19 Ω

so, a)  Highest Total Resistance :- 32 Ω  

     b) Lowest Total Resistance :- ≈ 1.19 Ω