### Correct Option: A (1:4) ### Explanation of the Answer A transformer is a device that transfers electrical energy between two or more circuits through electromagnetic induction. In a step-down transformer, the voltage is reduced from the primary coil to the secondary coil. The relationship between the number of turns in the primary and secondary coils and the voltages across them is given by the transformer equation: \[ \frac{V_p}{V_s} = \frac{N_p}{N_s} \] Where: - \( V_p \) = Voltage across the primary coil - \( V_s \) = Voltage across the secondary coil - \( N_p \) = Number of turns in the primary coil - \( N_s \) = Number of turns in the secondary coil #### Step-by-Step Calculation 1. **Identify the Given Values:** - Primary turns (\( N_p \)) = 200 turns - Secondary turns (\( N_s \)) = 50 turns - Primary voltage (\( V_p \)) = 120 V 2. **Apply the Transformer Equation:** We need to find the voltage ratio \( \frac{V_p}{V_s} \): \[ \frac{V_p}{V_s} = \frac{N_p}{N_s} \] 3. **Substitute the Values:** \[ \frac{V_p}{V_s} = \frac{200}{50} \] 4. **Calculate the Ratio:** \[ \frac{200}{50} = 4 \] This means: \[ \frac{V_p}{V_s} = 4 \quad \text{or} \quad V_p = 4 \cdot V_s \] 5. **Find the Voltage Across the Secondary Coil:** Rearranging the equation gives: \[ V_s = \frac{V_p}{4} = \frac{120V}{4} = 30V \] 6. **Determine the Voltage Ratio:** The voltage ratio \( \frac{V_p}{V_s} \) is 4:1, which can also be expressed as 1:4 when considering the ratio of primary to secondary. ### Why Other Options Are Incorrect - **Option B (4:1)**: This option is technically correct in terms of the ratio of primary to secondary voltage, but it does not match the question's request for the ratio in the form of primary to secondary (which is 1:4). Therefore, while it represents the same relationship, it does not answer the question as asked. - **Option C (1:2)**: This option suggests that the primary voltage is twice that of the secondary voltage. However, based on our calculations, the secondary voltage is actually 30V when the primary is 120V, which does not support this ratio. - **Option D (2:1)**: This option implies that the primary voltage is twice that of the secondary voltage. Again, this is incorrect as the primary voltage is four times the secondary voltage, not two times. ### Common Pitfalls - **Misunderstanding the Ratio**: Students often confuse the direction of the ratio. It’s important to express the ratio in the correct order as per the question's requirement. - **Forgetting to Simplify**: When calculating ratios, ensure that you simplify them correctly to their lowest terms. - **Confusing Step-Up and Step-Down Transformers**: Remember that in a step-down transformer, the primary voltage is higher than the secondary voltage, which is crucial for understanding the relationship between turns and voltage. ### Revision Summary - The voltage ratio in a transformer is determined by the ratio of the number of turns in the primary and secondary coils. - For a step-down transformer with 200 turns in the primary and 50 turns in the secondary, the voltage ratio is 1:4. - The primary voltage (120V) is four times the secondary voltage (30V). - Always express ratios in the correct order as per the question's requirement to avoid confusion.