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) The highest resistance is when the resistances are connected in series: R1 = 4 ohm R2 = 8 ohm R3 = 12 ohm R4 = 24 ohm Total resistance in series = R1 + R2 + R3 + R4 = 4 + 8 + 12 + 24 = 48 ohm Thus, highest resistance is 48 ohm. (b) The lowest resistance is when the resistances are connected in parallel Total resistance in parallel = 1/R1 + 1/R2 + 1/R3 + 1/R4 1/R = 1/2 + 1/8 + 1/12 + 1/24 = 12/24 1/R = 1/2 ohm, R = 2 ohm Thus, lowest resistance is 2 ohm.
