### Correct Option: A. The voltage is directly proportional to the number of turns. ### Detailed Explanation: In an ideal transformer, the relationship between the number of turns in the primary coil (N₁) and the secondary coil (N₂) and the voltages across them (V₁ for the primary and V₂ for the secondary) is described by the transformer equation: \[ \frac{V₁}{V₂} = \frac{N₁}{N₂} \] This equation tells us that the ratio of the primary voltage (V₁) to the secondary voltage (V₂) is equal to the ratio of the number of turns in the primary coil (N₁) to the number of turns in the secondary coil (N₂). #### Step-by-Step Breakdown: 1. **Understanding the Transformer**: A transformer consists of two coils of wire, the primary coil and the secondary coil, wound around a magnetic core. When an alternating current (AC) flows through the primary coil, it creates a changing magnetic field that induces a voltage in the secondary coil. 2. **Voltage and Turns Relationship**: The transformer equation can be rearranged to express the relationship between voltage and turns: \[ V₂ = V₁ \cdot \frac{N₂}{N₁} \] This shows that if you increase the number of turns in the secondary coil (N₂) while keeping the primary voltage (V₁) constant, the secondary voltage (V₂) will increase proportionally. Conversely, if you increase the number of turns in the primary coil (N₁), the secondary voltage (V₂) will decrease. 3. **Direct Proportionality**: The key takeaway is that the voltage across the coils is directly proportional to the number of turns. If you double the number of turns in the secondary coil, the voltage across it will also double, assuming the primary voltage remains constant. 4. **Ideal Transformer Assumption**: This relationship holds true under the assumption of an ideal transformer, which means there are no losses due to resistance, magnetic leakage, or other inefficiencies. In real-world applications, transformers are not ideal, but this basic principle still provides a good approximation. ### Why Other Options Are Incorrect: - **Option B: The voltage is inversely proportional to the number of turns.** - This option is incorrect because it misrepresents the relationship. The voltage is not inversely proportional; rather, it is directly proportional as explained above. If the number of turns increases, the voltage increases, not decreases. - **Option C: The voltage across the primary is equal to the voltage across the secondary.** - This statement is only true in a specific case where the number of turns in both coils is equal (N₁ = N₂). In general, the voltages can be different depending on the turns ratio. Therefore, this option is misleading and not universally applicable. - **Option D: The voltage across the primary is always greater than the voltage across the secondary.** - This option is incorrect because it assumes a specific scenario where the primary voltage is always higher, which is not true. Depending on the turns ratio, the secondary voltage can be greater than, less than, or equal to the primary voltage. For example, in a step-up transformer, the secondary voltage is greater than the primary voltage. ### Summary for Revision: - In an ideal transformer, the relationship between voltages and turns is given by \( \frac{V₁}{V₂} = \frac{N₁}{N₂} \). - Voltage is directly proportional to the number of turns in the coils. - An increase in the number of turns in the secondary coil results in a proportional increase in the secondary voltage. - The transformer operates under the assumption of no losses, making the ideal transformer model a useful approximation.