Govt. Exams
By maximum power transfer theorem, maximum power is transferred to external load when load resistance equals internal resistance
Due to symmetry, current divides into three paths of 1Ω each in parallel at the first vertex, then similar distribution at other vertices. Equivalent = 1/3 + 1/6 + 1/3 = 5/6Ω
When stretched, volume constant: A × L = A' × 2L → A' = A/2. New resistance R' = ρ(2L)/(A/2) = 4ρL/A = 4R.
Sensitivity θ ∝ NAB/k. It increases with more turns (N) and weaker torsional constant (k). Both B and C increase sensitivity.
Using potentiometer formula: E₁/40 = E₁'/(30) where E₁' = E₁/(1 + r/5) after adding external resistance. This gives: 40/(30) = (1 + r/5) → 4/3 = 1 + r/5 → r/5 = 1/3 → r = 5/3... Let me recalculate: r = 10/3 Ω.
The grounded sphere develops negative charge to maintain V = 0. The charge distribution is non-uniform because the near side accumulates more negative charge.
At midpoint, distance from each charge = 0.5 cm = 0.005 m. Both fields point in same direction (from +q toward -q). E_total = 2 × k × 2×10⁻⁶ / (0.005)² = 7.2 × 10⁷ V/m.
For a uniformly charged disc, the field at the center involves integrating contributions from rings. Result: E = σ/(2ε₀) = Q/(2πε₀R²).
All charge elements on the ring are equidistant from the axial point. Distance = √(R² + x²), so V = kQ/√(R² + x²).
Distance from each vertex to centroid is a/√3. V = k(q + q - 2q)/(a/√3) = 0. The charges sum to zero, giving zero potential.
