A transformer has 450 turns in its primary coil and 30 turns in its secondary coil. Which one of the following statements concerning this transformer is true?

Options

A. The turns ratio is 15 for this transformer.
B. The ratio of the voltages `V_(s)//V_(p)` is 15 for this transformer.
C. The ratio of the currents `I_(s)//I_(P)` is 0.067 for this transformer.
D. The power delivered to the secondary must be the same as that delivered to the primary.

Answer

To solve the problem regarding the transformer with 450 turns in the primary coil and 30 turns in the secondary coil, we will analyze the statements provided and determine which are true based on the principles of transformers.

### Step-by-Step Solution:

1. **Identify the Turns Ratio**:
- The number of turns in the primary coil (\(N_p\)) = 450
- The number of turns in the secondary coil (\(N_s\)) = 30
- The turns ratio is given by:
\[ \text{Turns Ratio} = \frac{N_p}{N_s} = \frac{450}{30} = 15 \]

2. **Check the Voltage Ratio**:
- The voltage ratio in a transformer is directly proportional to the turns ratio:
\[ \frac{V_s}{V_p} = \frac{N_s}{N_p} = \frac{30}{450} = \frac{1}{15} \]
- This means that the voltage in the secondary coil is \( \frac{1}{15} \) of the primary voltage.

3. **Check the Current Ratio**:
- According to the principle of conservation of energy, the current ratio is inversely proportional to the turns ratio:
\[ \frac{I_s}{I_p} = \frac{V_p}{V_s} = \frac{N_p}{N_s} = 15 \]
- Therefore, the secondary current is 15 times the primary current.

4. **Power Consideration**:
- The power in the primary coil (\(P_p\)) and the power in the secondary coil (\(P_s\)) must be equal in an ideal transformer:
\[ P_p = P_s \]
- Power can be expressed as:
\[ P = VI \]
- Thus, we can write:
\[ V_p I_p = V_s I_s \]
- Using the voltage and current ratios calculated, we can verify that the powers are equal.

### Conclusion:
From the analysis:
- The turns ratio is indeed 15, which confirms that the first statement is true.
- The voltage ratio is \( \frac{1}{15} \), which contradicts the second statement.
- The current ratio is 15, confirming the third statement is true.
- The power delivered to the secondary is not equal to that of the primary, making the fourth statement false.

Thus, the true statements are:
- The ratio of turns is 15 (True).
- The ratio of current is 15 (True).