### Correct Option: B. Vs = 0.5Vp ### 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: - \(Np = 100\) turns (primary coil) - \(Ns = 50\) turns (secondary coil) Now, substituting the 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 find \(Vs\): \[ Vs = \frac{Vp}{2} \] This means that the secondary voltage is half of the primary voltage: \[ Vs = 0.5Vp \] ### Why Other Options Are Incorrect: - **Option A: Vs = 2Vp** - 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 the number of turns in the primary is greater than in the secondary), the secondary voltage is always less than the primary voltage. - **Option C: Vs = Vp** - This option implies that the primary and secondary voltages are equal. This would only be true in a transformer where the number of turns in the primary and secondary coils are the same (Np = Ns). Since in this case, \(Np\) is greater than \(Ns\), this option is incorrect. - **Option D: Vs = 1.5Vp** - This option suggests that the secondary voltage is one and a half times the primary voltage. This is also incorrect as it does not reflect the turns ratio. The relationship derived from the turns ratio shows that the secondary voltage is actually less than the primary voltage. ### Summary of Key Concepts: - **Turns Ratio**: The ratio of the number of turns in the primary coil to the number of turns in the secondary coil determines the voltage relationship. - **Voltage Relationship**: For an ideal transformer, \( \frac{Vp}{Vs} = \frac{Np}{Ns} \). - **Step-Down Transformer**: When \(Np > Ns\), the secondary voltage is less than the primary voltage. - **Final Formula**: For this transformer, \(Vs = 0.5Vp\). ### Revision Summary: - In an ideal transformer, the voltage ratio is determined by the turns ratio. - The formula \( \frac{Vp}{Vs} = \frac{Np}{Ns} \) is crucial for understanding voltage relationships. - A step-down transformer has more turns in the primary than in the secondary, resulting in a lower secondary voltage. - Always check the turns ratio to determine if the secondary voltage will be higher or lower than the primary voltage.