### Correct Option: B. Vs = 0.25Vp ### Detailed Explanation: Transformers operate on the principle of electromagnetic induction and are used to change the voltage levels in alternating current (AC) circuits. The relationship between the primary voltage (Vp) and the secondary voltage (Vs) in a transformer is determined by the number of turns in the primary coil (Np) and the secondary coil (Ns). This relationship is given by the transformer equation: \[ \frac{Vs}{Vp} = \frac{Ns}{Np} \] 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 problem: - \( Np = 200 \) turns (primary coil) - \( Ns = 50 \) turns (secondary coil) Now, we can substitute these values into the transformer equation: \[ \frac{Vs}{Vp} = \frac{50}{200} \] Calculating the right side: \[ \frac{50}{200} = 0.25 \] This means: \[ \frac{Vs}{Vp} = 0.25 \] To express \( Vs \) in terms of \( Vp \), we can rearrange the equation: \[ Vs = 0.25 \times Vp \] Thus, the relationship between the primary voltage and the secondary voltage is: \[ Vs = 0.25Vp \] This confirms that the correct answer is **B. Vs = 0.25Vp**. ### Why Other Options Are Incorrect: - **Option A: Vs = 4Vp** - 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 \( Ns < Np \), the secondary voltage must be less than the primary voltage. - **Option C: Vs = 2Vp** - This option implies that the secondary voltage is double the primary voltage. Again, this is incorrect because it contradicts the turn ratio. With fewer turns in the secondary coil, the voltage cannot be greater than the primary voltage. - **Option D: Vs = 0.5Vp** - This option suggests that the secondary voltage is half of the primary voltage. While this could be true if the turns were in a 1:2 ratio, in this case, the ratio is 1:4 (50 turns to 200 turns), leading to a much smaller secondary voltage. ### Common Pitfalls: - **Misunderstanding the Turn 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. - **Forgetting to Rearrange the Formula**: When using the transformer equation, ensure you correctly rearrange it to find the desired variable. - **Assuming Direct Proportionality**: The relationship is not direct; it is based on the ratio of turns, which can lead to incorrect assumptions about voltage changes. ### Revision Summary: - The transformer equation relates primary and secondary voltages to the number of turns in the coils. - For this transformer, \( Vs = 0.25Vp \) because the secondary coil has fewer turns than the primary. - Always check the turn ratio to determine if the secondary voltage will be higher or lower than the primary voltage. - Remember that fewer turns in the secondary coil result in a lower voltage output.