Two resistances of 5.0 Ω and 7.0 Ω are connected in series and the combination is connected in parallel with a resistance of 36.0 Ω. The equivalent resistance of the combination of three resistors is 

CONCEPT:

Combination of Resistors

• When resistors are connected in series, their resistances add up. The total resistance of resistors in series (R_series) is given by:

  R_series = R₁ + R₂ + ... + R_n

• When resistors are connected in parallel, the reciprocal of the total resistance (R_parallel) is the sum of the reciprocals of the individual resistances:

  1/R_parallel = 1/R₁ + 1/R₂ + ... + 1/R_n

EXPLANATION:

• Given resistances: R₁ = 5.0 Ω, R₂ = 7.0 Ω (in series), and R₃ = 36.0 Ω (in parallel with the series combination).
• First, calculate the equivalent resistance of the series combination:
  • R_series = R₁ + R₂
  • = 5.0 Ω + 7.0 Ω
  • = 12.0 Ω
• Next, calculate the equivalent resistance of the parallel combination of R_series and R₃:
  • 1/R_parallel = 1/R_series + 1/R₃
  • = 1/12.0 Ω + 1/36.0 Ω
  • = 4/36.0 Ω
  • = 1/9.0 Ω
  • R_parallel = 9.0 Ω

Therefore, the equivalent resistance of the combination of the three resistors is 9.0 Ω.