To determine the relationship between the primary voltage (Vp) and the secondary voltage (Vs) in a step-down transformer, we can use the transformer equation, which relates the number of turns in the primary and secondary coils to their respective voltages. ### Step-by-Step Explanation 1. **Understanding the Transformer Equation**: The basic formula for a transformer is given by: \[ \frac{V_p}{V_s} = \frac{N_p}{N_s} \] where: - \( V_p \) = primary voltage - \( V_s \) = secondary voltage - \( N_p \) = number of turns in the primary coil - \( N_s \) = number of turns in the secondary coil 2. **Identifying the Given Values**: From the problem, we know: - \( N_p = 240 \) turns (primary coil) - \( N_s = 60 \) turns (secondary coil) 3. **Substituting the Values into the Equation**: Plugging the values into the transformer equation: \[ \frac{V_p}{V_s} = \frac{240}{60} \] 4. **Simplifying the Ratio**: Simplifying the right side: \[ \frac{240}{60} = 4 \] Therefore, we have: \[ \frac{V_p}{V_s} = 4 \] 5. **Rearranging the Equation**: To find the relationship between \( V_s \) and \( V_p \), we can rearrange the equation: \[ V_s = \frac{V_p}{4} \] This can also be expressed as: \[ V_s = 0.25 V_p \] ### Conclusion: Correct Option The correct answer is **B. Vs = 0.25Vp**. ### Explanation of Other Options - **A. Vs = 4Vp**: This option suggests that the secondary voltage is four times the primary voltage, which is incorrect for a step-down transformer. In a step-down transformer, the secondary voltage is always less than the primary voltage. - **C. Vs = 2Vp**: This option implies that the secondary voltage is twice the primary voltage, which is also incorrect. The relationship derived shows that the secondary voltage is a quarter of the primary voltage, not double. - **D. Vs = Vp**: This option states that the secondary voltage is equal to the primary voltage, which is not true for a step-down transformer. In a step-down transformer, the secondary voltage is always lower than the primary voltage. ### Common Pitfalls - **Confusing Step-Up and Step-Down Transformers**: Remember that a step-down transformer reduces voltage, while a step-up transformer increases voltage. - **Misapplying the Transformer Equation**: Ensure you correctly identify which coil is primary and which is secondary, as this affects the voltage relationship. - **Ignoring Turns Ratio**: Always pay attention to the turns ratio, as it directly influences the voltage transformation. ### Revision Summary - The transformer equation relates primary and secondary voltages to the number of turns in the coils. - For a step-down transformer with 240 turns in the primary and 60 turns in the secondary, the relationship is \( V_s = 0.25 V_p \). - The correct answer is **B. Vs = 0.25Vp**. - Always remember that in a step-down transformer, the secondary voltage is less than the primary voltage.