Practice question

**Series combination** R_eq = R₁+R₂+..., same current I through each, voltage divides proportionally V_i = I R_i. Parallel combination 1/R_p = 1/R₁+1/R₂+..., same voltage V across each, current divides inversely, equivalent R_p = (R₁ R₂)/(R₁+R₂) for two resistors. Parallel resistance: (1/R_p) = (1/3) + (1/6) + (1/9) = (6 + 3 + 2/18) = (11/18) ⇒ R_p = (18/11) ≈ 1.64 Ω . Total resistance: Rtₒtₐl = 2 + 1.64 = 3.64 Ω . Total current: I = (ε/Rtₒtₐl) = (12/3.64) ≈ 3.3 A . Voltage across parallel: V = I R_p = 3.3 × 1.64 ≈ 5.41 V . Current through 9 Ω :