### 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: \[ V_p = 2V_s \] 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, based on the turns ratio, the secondary voltage is actually half of the primary voltage when the secondary coil has fewer turns than the primary. - **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. Since the secondary coil has fewer turns, this option is incorrect. - **Option D: \(V_s = 50V_p\)** This option suggests that the secondary voltage is fifty times the primary voltage, which is not possible in a transformer. The relationship derived from the turns ratio shows that the secondary voltage is much smaller than the primary voltage in this case. ### Formulas and Common Pitfalls: - **Key Formula**: \[ \frac{V_p}{V_s} = \frac{N_p}{N_s} \] - **Common Pitfalls**: - Confusing the turns ratio: Remember that if the secondary coil has fewer turns than the primary, the secondary voltage will be lower. - Misapplying the formula: Always ensure you are using the correct relationship based on the turns ratio. ### Revision Summary: - In an ideal transformer, the voltage relationship is determined by the turns ratio. - The formula is \(\frac{V_p}{V_s} = \frac{N_p}{N_s}\). - For this problem, with \(N_p = 100\) and \(N_s = 50\), the relationship is \(V_s = 0.5V_p\). - Always check the turns ratio to determine whether the secondary voltage will be higher or lower than the primary voltage.