Which of the following is correct with reference to step up single-phase transformer?

Question

Examoogle · Accepted Answer

The correct answer is Option C: Turn ratio = Transformation ratio. In electrical machines, the turn ratio ($a$ or $k$) is defined as the ratio of primary turns to secondary turns ($N_1/N_2$), whereas the transformation ratio ($K$) is defined as the ratio of secondary turns to primary turns ($N_2/N_1$). For a transformer, these two terms are mathematically inverse to each other; however, in many standard textbooks and exam conventions, the term 'Turn ratio' is defined interchangeably with 'Transformation ratio' as $N_2/N_1$, making them identical.

Step-by-Step Solution & Concepts:
In electrical machines, the turn ratio ($a$ or $k$) is defined as the ratio of primary turns to secondary turns ($N_1/N_2$), whereas the transformation ratio ($K$) is defined as the ratio of secondary turns to primary turns ($N_2/N_1$). For a transformer, these two terms are mathematically inverse to each other; however, in many standard textbooks and exam conventions, the term 'Turn ratio' is defined interchangeably with 'Transformation ratio' as $N_2/N_1$, making them identical.

Working Principle: The transformer operates on Faraday's law of electromagnetic induction. The voltage induced in a winding is directly proportional to the number of turns, expressed as $V_1/V_2 = N_1/N_2$. When $N_2 > N_1$, the device acts as a step-up transformer, resulting in a transformation ratio $K > 1$.

Key Formulas: $$K = \frac{N_2}{N_1} = \frac{V_2}{V_1} = \frac{I_1}{I_2}$$ — transformation ratio where $K > 1$ for step-up; $$a = \frac{N_1}{N_2}$$ — turns ratio often used in power engineering

Key Points: For a step-up transformer, the secondary voltage is greater than the primary voltage ($V_2 > V_1$); The transformation ratio $K$ is greater than unity ($K > 1$) for a step-up transformer; The terms 'turns ratio' and 'transformation ratio' are frequently used synonymously in competitive exams, leading to the equality relation

Advantages: Voltage stepping for long-distance power transmission; Reduction in $I^2R$ losses due to higher transmission voltage

Disadvantages: Requires high insulation levels due to increased secondary voltage; Increased risk of corona effect in high voltage overhead lines

Applications: Power generating stations (Step-up from generator voltage to transmission voltage); HVDC converter stations

Additional Info: In a step-up transformer, $N_2 > N_1$, so $K = N_2/N_1 > 1$.. Options A, B, and D are incorrect because standard definitions in this curriculum context treat the ratios as identical numerical constants ($N_2/N_1$).

Answer: C is correct — In the context of standard electrical engineering examinations, the turns ratio and transformation ratio are numerically equal representations of the ratio $\frac{N_2}{N_1}$.

Exam Tip: Always verify if the question defines 'Turns Ratio' as $N_1/N_2$ or $N_2/N_1$ based on the specific textbook, but in most objective exams, expect the transformation ratio $K = N_2/N_1$ to be the standard reference.

Examoogle · Answer

Option A: Turn ratio ≠ Transformation ratio

Examoogle · Answer

Option B: Turn ratio > Transformation ratio

Examoogle · Answer

Option D: Turn ratio

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