Practice question
Question
Why does the terminal voltage of a battery become equal to its emf when no current flows?
Explanation
**Temperature dependence** of resistance R_t = R₀[1+α(T-T₀)], α temperature coefficient (per °C), R₀ resistance at T₀ (Ω). For metals α positive ≈10⁻³ /°C, resistance increases with temperature because τ decreases due to increased phonon scattering, n nearly constant. Terminal voltage V = ε - I r . When I = 0 (open circuit), the internal voltage drop I r = 0 , so V = ε , matching the emf. 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 No internal voltage drop,
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