Govt. Exams
Entrance Exams
R = ρL/A. R₁/R₂ = (L₁/L₂) × (A₂/A₁) = (2/3) × (2²/1²) = (2/3) × 4 = 8/3
E = V + Ir → 1.5 = 1.2 + 2r → 0.3 = 2r → r = 0.15Ω.
1/Req = 1/2 + 1/3 + 1/6 = 3/6 + 2/6 + 1/6 = 6/6 = 1. Therefore Req = 1Ω.
Resistivity ρ is an intrinsic property of material and varies with temperature. It is independent of geometry (length and area) and current/voltage.
Brown=1, Black=0, Red=2 (multiplier 10²), Gold=5% tolerance. Value = 10 × 10² = 1000Ω ± 5%.
For parallel resistances: 1/Req = 1/R₁ + 1/R₂ = 1/4 + 1/6 = 3/12 + 2/12 = 5/12. Therefore Req = 12/5 = 2.4Ω.
Drift velocity vd = I/(nAe) is typically 10⁻⁴ to 10⁻³ m/s for normal currents, much slower than thermal velocity (~10⁶ m/s) but much slower than light speed.
Resistivity of aluminum (2.65 × 10⁻⁸ Ω·m) is greater than copper (1.68 × 10⁻⁸ Ω·m). Since P = I²R and R = ρL/A, aluminum has higher resistance and thus higher power dissipation for same current.
Conductivity σ = 1/ρ where ρ is resistivity. Since resistivity is in Ω·m, conductivity is in (Ω·m)⁻¹ = S/m or mho/meter.
