### Correct Option: C (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 1: Understanding the Turns Ratio The relationship between the primary voltage (\(V_p\)) and the secondary voltage (\(V_s\)) in a transformer is given by the turns ratio, which is defined as: \[ \frac{V_p}{V_s} = \frac{N_p}{N_s} \] Where: - \(N_p\) = number of turns in the primary coil - \(N_s\) = number of turns in the secondary coil #### Step 2: Applying the Given Values In this problem: - \(N_p = 200\) turns (primary coil) - \(N_s = 50\) turns (secondary coil) Now, we can substitute these values into the formula: \[ \frac{V_p}{V_s} = \frac{200}{50} \] #### Step 3: Simplifying the Ratio Now, simplify the fraction: \[ \frac{200}{50} = 4 \] This means: \[ \frac{V_p}{V_s} = 4 \] This can be expressed as: \[ V_p : V_s = 4 : 1 \] ### Conclusion Thus, the ratio of the primary voltage to the secondary voltage in this step-down transformer is **4:1**. This means that for every 4 volts in the primary coil, there is 1 volt in the secondary coil. ### Explanation of Other Options: - **Option A (1:4)**: This suggests that the primary voltage is less than the secondary voltage, which contradicts the definition of a step-down transformer. In a step-down transformer, the primary voltage is always greater than the secondary voltage. - **Option B (2:1)**: This implies that the primary voltage is twice that of the secondary voltage. However, based on our calculations, the primary voltage is actually four times the secondary voltage, making this option incorrect. - **Option D (1:2)**: This suggests that the primary voltage is half of the secondary voltage, which again contradicts the operation of a step-down transformer. The primary voltage must be greater than the secondary voltage. ### Common Pitfalls: 1. **Confusing Step-Up and Step-Down Transformers**: Remember that in a step-down transformer, the primary voltage is always greater than the secondary voltage. 2. **Misinterpreting the Ratio**: Ensure you understand that the ratio \(V_p : V_s\) indicates how many times the primary voltage is compared to the secondary voltage. 3. **Forgetting to Simplify**: Always simplify the ratio to its lowest terms to avoid confusion. ### Revision Summary: - The turns ratio in a transformer determines the voltage ratio. - For a step-down transformer, \(V_p\) is greater than \(V_s\). - The formula for voltage ratio is \(\frac{V_p}{V_s} = \frac{N_p}{N_s}\). - In this case, with 200 turns in the primary and 50 in the secondary, the ratio is 4:1.