In an ideal transformer, a step-up transformer is designed primarily to increase which electrical quantity in the secondary coil?

Introduction / Context:
Transformers are widely used in electrical power systems to change voltage levels for efficient transmission and safe usage. There are two main types: step-up transformers, which raise voltage, and step-down transformers, which lower voltage. This question checks whether you know which electrical quantity a step-up transformer is intended to increase in its secondary winding.

Given Data / Assumptions:

• We are dealing with an ideal transformer working on alternating current (AC).
• The transformer has primary and secondary coils wound on a common core.
• A step-up transformer has more turns on the secondary than on the primary.
• We ignore energy losses and assume constant frequency.

Concept / Approach:
For an ideal transformer, the ratio of secondary voltage V2 to primary voltage V1 equals the ratio of secondary turns N2 to primary turns N1. In a step-up transformer, N2 is greater than N1, so V2 is greater than V1. Power (P = V * I) is conserved approximately (neglecting losses), meaning that if voltage increases, current decreases accordingly. The frequency of AC is determined by the source and does not change in a transformer. So the key purpose of a step-up transformer is to increase voltage in the secondary coil.

Step-by-Step Solution:
Step 1: Use the transformer turns relation: V2 / V1 = N2 / N1. Step 2: For a step-up transformer, N2 > N1, which implies V2 > V1. Step 3: For an ideal transformer, input power equals output power, so V1 * I1 ≈ V2 * I2. Step 4: If V2 is larger than V1, then I2 must be smaller than I1 to keep power nearly constant. Step 5: The AC frequency is determined by the supply and remains the same on both sides of the transformer. Step 6: Therefore, a step-up transformer is used primarily to increase the voltage in the secondary coil.

Verification / Alternative check:
In power transmission, electricity generated at power stations is stepped up to very high voltages (for example, hundreds of kilovolts) before being sent through long transmission lines. This reduces current and hence resistive losses in the wires. At the receiving end, step-down transformers reduce the high voltage to safer levels for domestic and industrial use. If step-up transformers increased current or power instead of voltage, this standard design of power grids would not work as it does. Textbook diagrams of transformers always show step-up devices raising voltage, not frequency or total power.

Why Other Options Are Wrong:
Power delivered: In an ideal transformer, power is conserved; the transformer does not create extra power.

Current in the secondary coil: For a step-up transformer, the current on the secondary side actually decreases compared to the primary.
Frequency of the alternating current: Transformers do not change the frequency; the input and output frequency remain the same.

Common Pitfalls:
A common misunderstanding is to think that a transformer that increases voltage also increases power. This would violate energy conservation. Another mistake is to assume that more turns always mean more current, but in transformers the voltage and current trade off to keep power roughly constant. Always remember: step-up means higher voltage and lower current; step-down means lower voltage and higher current.

Final Answer:
A step-up transformer increases the Voltage in the secondary coil.