### Correct Option: B. V_s = 0.5V_p ### Detailed Explanation: In an ideal transformer, the relationship between the primary voltage (\(V_p\)) and the secondary voltage (\(V_s\)) is determined by the turns ratio of the coils. The turns ratio is defined as the ratio of the number of turns in the primary coil (\(N_p\)) to the number of turns in the secondary coil (\(N_s\)). The formula that relates the primary and secondary voltages to the turns ratio 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 In this case: - \(N_p = 100\) turns (primary coil) - \(N_s = 50\) turns (secondary coil) Now, substituting the values into the formula: \[ \frac{V_p}{V_s} = \frac{100}{50} = 2 \] This means that: \[ V_p = 2V_s \] To find the relationship for \(V_s\), we can rearrange the equation: \[ V_s = \frac{V_p}{2} \] This can also be expressed as: \[ V_s = 0.5V_p \] Thus, the correct relationship is \(V_s = 0.5V_p\), which corresponds to option B. ### Why Other Options Are Incorrect: - **Option A: \(V_s = 2V_p\)** This option suggests that the secondary voltage is double the primary voltage. This is incorrect because, in a step-down transformer (which this is, since \(N_s < N_p\)), the secondary voltage is less than the primary voltage. - **Option C: \(V_s = V_p\)** This option implies that the primary and secondary voltages are equal. This is only true in a transformer with equal turns in both coils (i.e., \(N_p = N_s\)). Since \(N_p\) is greater than \(N_s\) in this case, this option is incorrect. - **Option D: \(V_s = 1.5V_p\)** This option suggests that the secondary voltage is one and a half times the primary voltage. This is not possible in a transformer with a turns ratio of 2:1 (as derived above). Therefore, this option is also incorrect. ### Common Pitfalls: 1. **Confusing Step-Up and Step-Down Transformers**: Remember that if the number of turns in the primary coil is greater than in the secondary coil, it is a step-down transformer, and the secondary voltage will be lower than the primary voltage. 2. **Misapplying the Turns Ratio**: Always ensure you are using the correct formula and substituting the values accurately. The turns ratio directly affects the voltage ratio. 3. **Ignoring Ideal Conditions**: The explanation assumes an ideal transformer with no losses. In real-world applications, factors like resistance and magnetic losses can affect the actual voltages. ### Revision Summary: - In an ideal transformer, the voltage ratio is determined by the turns ratio: \(\frac{V_p}{V_s} = \frac{N_p}{N_s}\). - For a transformer with 100 turns in the primary and 50 turns in the secondary, the relationship is \(V_s = 0.5V_p\). - A step-down transformer has fewer turns in the secondary coil, resulting in a lower secondary voltage compared to the primary voltage. - Always check the turns ratio to determine whether the transformer is stepping up or stepping down the voltage.