Govt. Exams
Heating increases atomic vibrations, leading to increased collisions between electrons and atoms, thus increasing resistance
E - I×r = V_terminal. 2 - I×0.5 = 1.8. I×0.5 = 0.2. I = 0.4A
At balance: R₁/R₂ = L₁/L₂. R₂ = R₁ × L₂/L₁ = 12 × 60/40 = 12 × 1.5... Wait: R₂ = 12 × (100-40)/40 = 12 × 60/40 = 18Ω. Actually checking: 12/R₂ = 40/60, so R₂ = 12 × 60/40 = 18Ω... Let me recalculate: R₁/R₂ = 40/60, 12/R₂ = 40/60, R₂ = 18Ω. If reversed: R₂ = 8Ω works when 12/8 = 60/40
EMF is proportional to balancing length. If EMF becomes E/2, balancing length becomes 75/2 = 37.5 cm
In series, current is same. V₁/V₂ = R₁/R₂ = 2R₂/R₂ = 2. Therefore V₂ = V₁/2 = 8/2 = 4V
At balance: P/Q = R/S. Therefore S = (Q × R)/P = (20 × 15)/10 = 30Ω
Each side has resistance 1.25Ω. Between adjacent corners: one path has 1.25Ω, parallel path has 3.75Ω. R_eq = (1.25 × 3.75)/(1.25 + 3.75) = 1.25Ω
When stretched to double length, volume remains constant. New area = A/2. R' = ρL'/A' = ρ(2L)/(A/2) = 4ρL/A = 4R
R = ρL/A = (1.7 × 10⁻⁸ × 0.1)/(0.02 × 0.03) = (1.7 × 10⁻⁹)/(6 × 10⁻⁴) = 2.83 × 10⁻⁷ Ω
Shunt formula: S = (G × I_g)/(I - I_g) = (100 × 0.01)/(1 - 0.01) = 1/0.99 ≈ 1.01Ω
