Question

what is (a) the highest, (b) the lowest total resistance tht can be secured by combinations of four coils of resistance 4 ohm, 8 ohm, 12 ohm, 24 ohm?

Answer 1

R1 ≈ 4 ohms

R2 ≈ 8 ohms

R3 ≈ 12 ohms

R4 ≈ 24 ohms

(a) If the coils are connected in a series then the equivalent resistance will be the highest as R ≈ R1+R2+R3+R4

                             R ≈ 4+8+12+24

                             R ≈ 48 ohms

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

1/R ≈ 1/R1+1/R2+1/R3+1/R4

1/R ≈ 1/4+1/8+1/12+1/24

    LCM of 4,8,12 and 24 ≈ 48

⇒  1/R ≈  12+6+4+2/48

1/R ≈  24/48

1/R ≈ 1/2

∴ R ≈ 2 ohms

2 ohms is the lowest total resistance.

   

Answer 2

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