### Correct Option: B (4:1) ### Explanation: A transformer is a device that transfers electrical energy between two or more circuits through electromagnetic induction. In a step-down transformer, the primary coil has more turns than the secondary coil, which results in a decrease in voltage from the primary to the secondary side. #### Step-by-Step Explanation: 1. **Understanding Turns Ratio**: - The turns ratio of a transformer is defined as the ratio of the number of turns in the primary coil (N₁) to the number of turns in the secondary coil (N₂). - This ratio is crucial because it directly relates to the voltages in the primary (V₁) and secondary (V₂) coils. \[ \text{Turns Ratio} = \frac{N₁}{N₂} \] 2. **Given Values**: - Primary coil turns (N₁) = 120 - Secondary coil turns (N₂) = 30 3. **Calculating the Turns Ratio**: - Plugging in the values into the turns ratio formula: \[ \text{Turns Ratio} = \frac{120}{30} = 4 \] 4. **Voltage Ratio**: - The relationship between the turns ratio and the voltage ratio in a transformer is given by: \[ \frac{V₁}{V₂} = \frac{N₁}{N₂} \] - Therefore, substituting the turns ratio we calculated: \[ \frac{V₁}{V₂} = 4 \] - This means that the primary voltage (V₁) is 4 times the secondary voltage (V₂). 5. **Final Ratio**: - The ratio of the primary voltage to the secondary voltage is thus: \[ V₁ : V₂ = 4 : 1 \] ### Why Other Options Are Incorrect: - **Option A (1:4)**: - This suggests that the primary voltage is one-fourth of the secondary voltage, which is incorrect. In a step-down transformer, the primary voltage is higher than the secondary voltage. - **Option C (1:3)**: - This implies that the primary voltage is one-third of the secondary voltage. This does not align with the turns ratio we calculated, which indicates a primary voltage that is higher than the secondary voltage. - **Option D (3:1)**: - This suggests that the primary voltage is three times the secondary voltage. While this is a plausible ratio, it does not match the calculated ratio of 4:1 based on the turns of the coils. ### Common Pitfalls: - **Confusing Step-Up and Step-Down Transformers**: Remember that in a step-down transformer, the primary voltage is always greater than the secondary voltage. - **Miscalculating the Turns Ratio**: Ensure you correctly identify which coil is primary and which is secondary before calculating the turns ratio. - **Ignoring the Relationship Between Voltage and Turns**: Always remember that the voltage ratio is directly proportional to the turns ratio. ### Revision Summary: - In a step-down transformer, the primary coil has more turns than the secondary coil. - The turns ratio (N₁/N₂) determines the voltage ratio (V₁/V₂). - For this transformer, the turns ratio is 4:1, meaning the primary voltage is 4 times the secondary voltage. - The correct answer is B (4:1).