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

(a) To obtain the highest resistance, connect the coils in series,

R_S = R₁ + R₂ + R₃ + R₄

= 4 + 8 + 12 + 24

= 48 Ω

‍

(b) To obtain the lowest resistance, connect the coils in parallel,

1/R_P = 1/R₁ + 1/R₂ + 1/R₃ + 1/R₄

1/R_P = 1/4 + 1/8 + 1/12 + 1/24

1/R_P = 1/4 ( 1 + 1/2 + 1/3 + 1/6)

1/R_P = 1/4 ((6 + 3 + 2 + 1) /6)

1/R_P = 1/4 (12/6)

1/R_P = 1/4 (2)

1/R_P = 1/2

R_P = 2 Ω

Chapter 11