To solve the problem of finding the number of turns \( N \) in the primary coil of a transformer, we can use the transformer equation, which relates the voltages and the number of turns in the primary and secondary coils. The equation is given by: \[ \frac{V_p}{V_s} = \frac{N_p}{N_s} \] Where: - \( V_p \) is the voltage across the primary coil, - \( V_s \) is the voltage across the secondary coil, - \( N_p \) is the number of turns in the primary coil, - \( N_s \) is the number of turns in the secondary coil. ### Given Data: - \( V_p = 120 \, \text{V} \) (voltage of the primary coil) - \( V_s = 1200 \, \text{V} \) (voltage of the secondary coil) - \( N_s = 1000 \) (number of turns in the secondary coil) ### Step-by-Step Solution: 1. **Set Up the Transformer Equation**: We can rearrange the transformer equation to solve for \( N_p \): \[ N_p = N_s \cdot \frac{V_p}{V_s} \] 2. **Substitute the Known Values**: Now, substitute the known values into the equation: \[ N_p = 1000 \cdot \frac{120}{1200} \] 3. **Calculate the Fraction**: First, calculate the fraction: \[ \frac{120}{1200} = \frac{1}{10} \] 4. **Multiply by the Number of Turns in the Secondary Coil**: Now, substitute this back into the equation: \[ N_p = 1000 \cdot \frac{1}{10} = 100 \] 5. **Final Answer**: Therefore, the value of \( N \) (the number of turns in the primary coil) is: \[ N = 100 \] ### Explanation of the Correct Answer: The correct option is **B. 100**. This is derived from the relationship between the primary and secondary voltages and the number of turns in the coils. The transformer equation shows that the voltage ratio is directly proportional to the turns ratio. Since the secondary voltage is ten times the primary voltage, the number of turns in the primary must be one-tenth of the number of turns in the secondary. ### Explanation of Incorrect Options: - **A. 120**: This option is incorrect because it does not satisfy the transformer equation. If \( N_p \) were 120, the calculated secondary voltage would not match the given 1200 V. - **C. 1000**: This option is incorrect because it suggests that the primary coil has the same number of turns as the secondary coil, which would imply that the primary voltage is equal to the secondary voltage, contradicting the given values. - **D. 1200**: This option is also incorrect as it would imply a primary voltage of 1200 V, which is not the case. The primary voltage is given as 120 V, and having 1200 turns in the primary would lead to a much higher secondary voltage than what is provided. ### Revision Summary: - Use the transformer equation \( \frac{V_p}{V_s} = \frac{N_p}{N_s} \) to relate voltages and turns. - Substitute known values carefully to find the unknown. - Ensure that the calculated values are consistent with the physical principles of transformers. - Remember that the turns ratio directly affects the voltage ratio in transformers.