We want to construct a transformer that decreases the voltage 4 times. If the number of turns in the secondary coil is 1680. What must be the number of turns in primary coil?

Options

A. 420
B. 840
C. 3360
D. 6720

Explanation

To solve the problem of finding the number of turns in the primary coil of a transformer that decreases the voltage by a factor of 4, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Transformer Relationship**:
The relationship between the primary voltage (Vp), secondary voltage (Vs), primary turns (Np), and secondary turns (Ns) in a transformer is given by the formula:
\[ \frac{Vp}{Vs} = \frac{Np}{Ns} \]

2. **Identify Given Values**:
- The transformer decreases the voltage by 4 times, which means:
\[ \frac{Vs}{Vp} = \frac{1}{4} \quad \text{or} \quad \frac{Vp}{Vs} = 4 \]
- The number of turns in the secondary coil (Ns) is given as 1680.

3. **Substituting Values into the Formula**:
Using the relationship from step 1 and substituting the known values:
\[ \frac{Vp}{Vs} = \frac{Np}{Ns} \]
becomes:
\[ 4 = \frac{Np}{1680} \]

4. **Solve for Np**:
Rearranging the equation to find Np:
\[ Np = 4 \times 1680 \]
Now, calculate Np:
\[ Np = 6720 \]

5. **Conclusion**:
The number of turns in the primary coil (Np) must be 6720.

### Final Answer:
The number of turns in the primary coil is **6720**.

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