Maximum efficiency of a transformer for a constant load current , occurs at

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Examoogle · Accepted Answer

unity p.f

Explanation: The maximum efficiency of a transformer occurs when the variable losses (copper losses) are exactly equal to the constant losses (iron or core losses). For a fixed load current, the copper loss is constant, and to maximize the overall efficiency, the transformer must deliver maximum active power for that current, which happens when the power factor is unity.

Working Principle: Efficiency ($\eta$) is defined as the ratio of output power to input power. Since Input = Output + Core Losses + Copper Losses, minimizing the loss components relative to the output for a fixed current requires the output power ($VI \cos\phi$) to be maximized. Since $V$ and $I$ are constant, efficiency is maximized when $\cos\phi = 1$.

Key Formulas: $\eta = \frac{VI \cos\phi}{VI \cos\phi + P_i + I^2R_e}$ — Transformer efficiency formula; $P_i = I^2R_e$ — Condition for maximum efficiency (Core loss = Copper loss)

Key Points: Maximum efficiency occurs when iron losses equal copper losses.; For a constant load current, the copper loss is fixed.; Unity power factor ensures the minimum kVA rating is required to supply a specific amount of real power.; Transformers are designed to operate at maximum efficiency near their full load.

Advantages: Optimizes energy utilization; Reduces heat dissipation in the core and windings

Disadvantages: Cannot maintain max efficiency across all load variations; Requires constant cooling system monitoring

Applications: Power grid distribution; Industrial motor drives

Additional Info: Core losses (eddy current and hysteresis) are constant regardless of load current.. Copper losses ($I^2R$) vary with the square of the load current.. Operating at a lagging power factor increases the current required to deliver the same active power, thereby increasing copper losses and reducing efficiency.

Answer: D is correct — Efficiency is maximized when the output power is purely active power, which occurs at unity power factor.

Exam Tip: Always remember that for a transformer, maximum efficiency occurs at a load where $P_{iron} = P_{copper}$, but for a specific fixed current, maximizing power delivered is the goal of the unity power factor.

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