Practice question
Question
A \( 40 \, \text{V} \) battery with negligible internal resistance is connected to a cubical network of
12 resistors, each \( 4 \, \Omega \). What is the total current?
Explanation
**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. Equivalent resistance: Rₑq = (5/6) R = (5/6) × 4 = (20/6) ≈ 3.33 Ω . Total current: I = (V/Rₑq) = (40/(20/6)) = 40 × (6/20) = 12 A . Applying I = n e A v_d, R = ρ l/A, R_t = R₀[1+αΔT], Kirchhoff's ΣI=0, ΣV=0, R_eq series/parallel, V = ε - I r and P = I²R, evaluation yields 12.0 A,
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