In a circuit with parallel branches, why does the branch with the lowest resistance carry the highest current?
**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. In parallel, voltage across each branch is the same ( V ). Current I = V / R , so the branch with the lowest R has the highest I , as current is inversely proportional to resistance. 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,
Ref: NCERT > Physics Book > Current Electricity > Temperature Dependence of Resistance and Resistivity