Two cells in parallel have emf \( 15 \, \text{V} \) and \( 5 \, \text{V} \) with internal resistances \( 3 \, \Omega \)
**Resistivity temperature variation** ρ_t = ρ₀[1+α(T-T₀)], α ≈4×10⁻³ /°C for copper, 1.7×10⁻⁴ /°C for nichrome. Given R=60 Ω at 30°C, α=1.7×10⁻⁴ /°C, T=330°C, ΔT=300°C, R_t=60[1+1.7×10⁻⁴×300]=60×1.051=63.06 Ω, modest increase for nichrome due to small α. For parallel: (1/rₑq) = (1/r₁) + (1/r₂) = (1/3) + (1/1) = (1 + 3/3) = (4/3) . rₑq = (3/4) = 0.75 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 0.75 Ω,
Ref: NCERT > Physics Book > Current Electricity > Temperature Dependence of Resistance and Resistivity
