### Correct Option: A. Vs = 0.5 Vp ### Detailed Explanation: In an ideal transformer, the relationship between the primary voltage (Vp) and the secondary voltage (Vs) 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 (Np) to the number of turns in the secondary coil (Ns). The formula that relates the primary and secondary voltages to the turns ratio is given by: \[ \frac{Vp}{Vs} = \frac{Np}{Ns} \] Where: - \(Vp\) = Primary voltage - \(Vs\) = Secondary voltage - \(Np\) = Number of turns in the primary coil - \(Ns\) = Number of turns in the secondary coil In this case, we have: - \(Np = 100\) turns (primary coil) - \(Ns = 50\) turns (secondary coil) Now, substituting these values into the formula: \[ \frac{Vp}{Vs} = \frac{100}{50} \] This simplifies to: \[ \frac{Vp}{Vs} = 2 \] From this, we can rearrange the equation to express \(Vs\) in terms of \(Vp\): \[ Vs = \frac{Vp}{2} \] This can also be written as: \[ Vs = 0.5 \, Vp \] Thus, the relationship between the primary voltage and the secondary voltage in this ideal transformer is that the secondary voltage is half of the primary voltage, confirming that option A is correct. ### Why Other Options Are Incorrect: - **Option B: Vs = 2 Vp** - This option suggests that the secondary voltage is double the primary voltage. This would only be true if the secondary coil had more turns than the primary coil, which is not the case here. Since the secondary coil has fewer turns, the voltage must be lower, not higher. - **Option C: Vs = Vp** - This option implies that the primary and secondary voltages are equal. This would only occur in a transformer with equal numbers of turns in both coils. Since the primary coil has 100 turns and the secondary has 50, this option is incorrect. - **Option D: Vs = 1.5 Vp** - This option suggests that the secondary voltage is 1.5 times the primary voltage. This is not consistent with the turns ratio we calculated. The secondary voltage must be lower than the primary voltage due to the fewer turns in the secondary coil. ### Summary of Key Points: - In an ideal transformer, the voltage ratio is directly related to the turns ratio of the coils. - The formula relating primary and secondary voltages is \( \frac{Vp}{Vs} = \frac{Np}{Ns} \). - For this transformer, with 100 turns in the primary and 50 turns in the secondary, the relationship is \( Vs = 0.5 \, Vp \). - Always remember that fewer turns in the secondary coil result in a lower voltage compared to the primary coil.