Govt. Exams
Entrance Exams
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
E/E_std = L/L_std, so E = 1.018 × (60/50) = 1.018 × 1.2 = 1.2216 ≈ 1.221 V
Total EMF = 1.5 + 1.5 = 3V. Total resistance = 2 + 0.5 + 0.5 = 3Ω. Current = 3/3 = 1A. Hmm, that's option C. Let me verify: I = 3V/5Ω = 0.6A
R = ρL/A. New resistance = ρ(L/2)/(A/2) = ρL/A = R. Actually R' = ρL'/A' where same ρ applies. R' = (L/2)/(A/2) × (ρ/A) × L = R. Recalculating: R' = ρ(L/2)/(A/2) = ρL/A × (1/2)/(1/2)⁻¹ = 2R
Terminal voltage V = E - Ir. Since I = E/(R+r), we get V = E - Er/(R+r) = ER/(R+r). Both expressions are equivalent
At null point: X/S = L₁/(100-L₁), so 20/S = 40/60, therefore S = 20 × 60/40 = 30Ω. Wait, let me recalculate: S = 20 × 60/40 = 30Ω. Correction needed - answer should be 30Ω if calculation is 20/S = 40/60
Potential gradient = V/L = 2V / 100cm = 0.02 V/cm