Practice question
Question
A \( 20 \, \text{V} \) battery with \( 2 \, \Omega \) internal resistance delivers a current of \( 2.5
\, \text{A} \) to a resistor. What is the resistance of the resistor?
Explanation
**Cells combination** series ε_eq = Σ ε_i, r_eq = Σ r_i, parallel for identical cells ε_eq = ε, r_eq = r/n, n number of cells. Maximum current when external R = r_eq, power transfer theorem, explaining why matching resistances maximizes power. Terminal voltage: V = ε - I r = 20 - 2.5 × 2 = 15 V . Resistance: R = (V/I) = (15/2.5) = 6 Ω . 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 6.0 Ω,
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