The best place to install a capacitor is

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across the terminals of inductive load

Explanation: The optimal installation point for power factor correction capacitors is directly across the terminals of the inductive load. This configuration minimizes the circulation of reactive current throughout the distribution wiring, significantly reducing $I^2R$ losses and voltage drops.

Working Principle: Inductive loads (like motors) draw lagging reactive current ($I_L$) from the supply, which lowers the overall power factor. By placing a capacitor in parallel, the capacitor provides a leading reactive current ($I_C$) locally at the load terminals. This results in the cancellation of the magnetizing current component, meaning the supply lines only carry the active power current ($I_P$), effectively improving the power factor at the source.

Key Formulas: $Q_C = P(	an \phi_1 - 	an \phi_2)$ — Required reactive power of capacitor to improve PF from $\cos \phi_1$ to $\cos \phi_2$; $I_{total} = \sqrt{I_R^2 + (I_L - I_C)^2}$ — Total line current with compensation

Key Points: Reduces current drawn from the utility grid.; Decreases power losses in transmission and distribution cables ($P_{loss} \propto I^2$).; Improves voltage regulation at the load end.; Prevents penalties for low power factor in industrial tariff structures.

Advantages: Lower line current leads to smaller wire sizes and less heating.; Better utilization of transformer and generator KVA capacity.; Reduced electricity bills due to improved PF.

Disadvantages: High initial cost for high-capacity capacitor banks.; Potential for over-correction leading to leading power factor at light loads.; Harmonic resonance risk if capacitors interact with system inductance.

Applications: Industrial induction motors; Power distribution transformers; Welding machines and arc furnaces

Additional Info: Installing capacitors at the load end is known as 'Individual Compensation'.. Installing at the main distribution board is 'Group Compensation', and at the substation is 'Central Compensation'.. Options A and C are technically inferior because they do not prevent reactive current flow in the feeder cables between the load and the capacitor.

Answer: B is correct — Placing capacitors across the terminals of the inductive load ensures that reactive power is neutralized at the point of origin, maximizing efficiency.

Exam Tip: Always remember: for maximum system efficiency, compensate reactive power as close to the load as physically possible to minimize 'I' in the $I^2R$ loss equation across the distribution lines.

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