It is possible to attain maximum efficiency in a transformer when the

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Examoogle · Accepted Answer

core losses are equal to rated full load copper losses

Explanation: Maximum efficiency in a transformer occurs when the variable losses (copper losses) are equal to the constant losses (core or iron losses). This is a consequence of setting the derivative of the efficiency equation with respect to load current to zero.

Working Principle: The efficiency $\eta$ of a transformer is given by $\eta = \frac{n S \cos \phi}{n S \cos \phi + P_i + n^2 P_{cu}}$, where $n$ is the fraction of full load, $S$ is the kVA rating, $P_i$ is core loss, and $P_{cu}$ is full load copper loss. Differentiating with respect to $n$ and setting to zero yields $n^2 P_{cu} = P_i$, which implies that the load-dependent copper loss must equal the load-independent core loss.

Key Formulas: $P_{cu,var} = P_i$ — Condition for maximum efficiency; $\eta = \frac{n S \cos \phi}{n S \cos \phi + P_i + n^2 P_{cu}}$ — General efficiency equation

Key Points: Core losses are constant regardless of load current.; Copper losses are proportional to the square of the load current ($I^2R$).; Maximum efficiency occurs at a specific fraction 'n' of the full load.; For most transformers, max efficiency is designed to occur near 50-75% of full load.

Advantages: Minimizes heat dissipation at operating load.; Optimizes material usage for specific power ratings.

Disadvantages: Requires precise transformer design during manufacturing.; Efficiency drops if the load deviates significantly from the designed 'n' value.

Applications: Power system planning for steady loads.; Transformer rating optimization in distribution networks.

Additional Info: Core loss ($P_i$) comprises hysteresis and eddy current losses.. Copper loss ($P_{cu}$) comprises $I^2R$ losses in primary and secondary windings.. Option B is incorrect because unequal losses lead to non-optimal energy conversion.. Option C is incorrect because copper losses are inherently variable with load, not constant.

Answer: A is correct — Maximum efficiency is achieved when the variable copper losses equal the constant core losses.

Exam Tip: Always remember that for any machine (DC motors or transformers), maximum efficiency occurs when the variable losses equal the constant losses.

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