### Correct Option: B. Vs = Vp × 0.25 ### Explanation: In a transformer, the relationship between the primary voltage (Vp) and the secondary voltage (Vs) is determined by the turns ratio of the coils. The formula that describes this relationship is: \[ \frac{Vs}{Vp} = \frac{Ns}{Np} \] Where: - \(Vs\) = Secondary voltage - \(Vp\) = Primary voltage - \(Ns\) = Number of turns in the secondary coil - \(Np\) = Number of turns in the primary coil In this case: - The primary coil has \(Np = 200\) turns. - The secondary coil has \(Ns = 50\) turns. Now, we can substitute these values into the formula: \[ \frac{Vs}{Vp} = \frac{50}{200} \] This simplifies to: \[ \frac{Vs}{Vp} = \frac{1}{4} \] From this, we can express \(Vs\) in terms of \(Vp\): \[ Vs = Vp \times \frac{1}{4} \] This means: \[ Vs = Vp \times 0.25 \] Thus, the correct relationship is \(Vs = Vp \times 0.25\), confirming that option B is correct. ### Why Other Options Are Incorrect: - **Option A: Vs = Vp × 4** - This option suggests that the secondary voltage is four times the primary voltage. This would imply that the secondary coil has 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 × 2** - This option implies that the secondary voltage is double the primary voltage. Again, this is incorrect because it contradicts the turns ratio. With fewer turns in the secondary coil, the voltage cannot be greater than the primary voltage. - **Option D: Vs = Vp × 0.5** - This option suggests that the secondary voltage is half of the primary voltage. While this could be true in a different turns ratio scenario, it does not apply here since the turns ratio indicates that the secondary voltage is actually one-fourth of the primary voltage. ### Common Pitfalls: - **Misunderstanding the Turns Ratio**: Students often confuse the relationship between the number of turns and the voltage. Remember, if the secondary coil has fewer turns than the primary, the secondary voltage will be lower. - **Ignoring Ideal Conditions**: The question assumes ideal conditions, meaning no energy losses. In real transformers, losses can occur, but for this problem, we assume perfect efficiency. - **Confusing Voltage and Current Relationships**: While this question focuses on voltage, remember that transformers also have a current relationship given by the inverse of the turns ratio. ### Revision Summary: - The relationship between primary and secondary voltages in a transformer is given by the turns ratio. - For a transformer with 200 turns in the primary and 50 turns in the secondary, the secondary voltage is one-fourth of the primary voltage. - The correct formula is \(Vs = Vp \times 0.25\). - Always remember that fewer turns in the secondary coil result in a lower voltage compared to the primary coil.