Question

Two unknown resistors A and B are connected together. When they are connected in series their combined resistance is 7 Ω. When they are connected in parallel, their combined resistance is 1.43 Ω. What are the resistances of A and B?

Select one:

a. 2.5 Ω and 4.5 Ω

b. 1 Ω and 6 Ω

c. 1.5 Ω and 5.5 Ω

d. 2 Ω and 5 Ω

e. 3 Ω and 4 Ω

Answer 1

Resistance of resistor A = R₁

Resistance of resistor B = R₂

Resistance when the resistors A and B are connected in series = R_s = 7

R_s = R₁ + R₂

R₁ = R_s - R₂

Resistance when the resistors A and B are connected in parallel = R_p = 1.43

R₁R₂ = R_sR_p

(R_s - R₂)R₂ = R_sR_p

(7 - R₂)R₂ = (7)(1.43)

7R₂ - R₂² = 10

R₂² - 7R₂ + 10 = 0

R₂ = 5 or 2

R₁ = R_s - R₂

R₁ = 7 - R₂

R₁ = 2 or 5

Resistances of A and B = 2 and 5