A transfomer has 500 primary tunrs and 10 secondary turns. If the secondary has a resistive load respectively, are

Options

A. `0.16 A, 3.2 xx 10^(-3)A`
B. `3.2 xx 10^(-3)` A, 0.16 A
C. `0.16 A, 0.16 A`
D. `3.2 xx 10^(-3)A, 3.2 xx 10^(-3)`A

Explanation

To solve the problem regarding the transformer with 500 primary turns and 10 secondary turns, we need to find the relationship between the primary current (Iₚ) and the secondary current (Iₛ).

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Number of primary turns (Nₚ) = 500
- Number of secondary turns (Nₛ) = 10

2. **Use the Transformer Turn Ratio:**
The relationship between the number of turns and the currents in a transformer is given by the equation:
\[ \frac{Nₛ}{Nₚ} = \frac{Iₚ}{Iₛ} \]
Substituting the known values:
\[ \frac{10}{500} = \frac{Iₚ}{Iₛ} \]

3. **Simplify the Ratio:**
Simplifying the left side:
\[ \frac{10}{500} = \frac{1}{50} \]
Thus, we have:
\[ \frac{1}{50} = \frac{Iₚ}{Iₛ} \]

4. **Express Iₛ in Terms of Iₚ:**
From the equation above, we can express the secondary current in terms of the primary current:
\[ Iₛ = 50 \cdot Iₚ \]

5. **Check the Options:**
We need to check which of the provided options satisfies this relationship. The options are given as pairs of (Iₚ, Iₛ).

- **Option A:** (0.16 A, 3.2 mA)
- **Option B:** (3.2 mA, 0.16 A)
- **Option C:** (Iₚ = Iₛ)
- **Option D:** (Iₚ = Iₛ)

We will convert the units where necessary:
- 3.2 mA = 0.0032 A

6. **Calculate Iₛ for Each Option:**
- **Option A:**
- If Iₚ = 0.16 A, then Iₛ = 50 * 0.16 = 8 A (not matching 3.2 mA)
- **Option B:**
- If Iₚ = 3.2 mA (0.0032 A), then Iₛ = 50 * 0.0032 = 0.16 A (matches)
- **Option C and D:**
- Both have equal currents, which does not satisfy our derived relationship.

7. **Conclusion:**
The only option that satisfies the relationship \( Iₛ = 50 \cdot Iₚ \) is **Option B**.

### Final Answer:
**Option B** is the correct answer: (Iₚ = 3.2 mA, Iₛ = 0.16 A).