A transformer has `100` turns in the primary coil and carries `8A` current. If input power is one kilowatt, the number of turns required in the secondary coil to have `500V` output will be

Options

A. 100
B. 200
C. 400
D. 300

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Identify the given values
- Number of turns in the primary coil (Np) = 100 turns
- Current in the primary coil (Ip) = 8 A
- Input power (PI) = 1 kW = 1000 W
- Output voltage (Vs) = 500 V

### Step 2: Calculate the primary voltage (Vp)
Using the formula for power:
\[ P = V \times I \]
We can rearrange this to find the primary voltage (Vp):
\[ Vp = \frac{P}{Ip} \]
Substituting the values:
\[ Vp = \frac{1000 \text{ W}}{8 \text{ A}} = 125 \text{ V} \]

### Step 3: Use the transformer turns ratio
The relationship between the number of turns and the voltages in a transformer is given by:
\[ \frac{Np}{Ns} = \frac{Vp}{Vs} \]
Where:
- Ns = number of turns in the secondary coil (which we need to find)

### Step 4: Substitute the known values into the turns ratio equation
Substituting the known values into the equation:
\[ \frac{100}{Ns} = \frac{125}{500} \]

### Step 5: Cross-multiply to solve for Ns
Cross-multiplying gives:
\[ 100 \times 500 = 125 \times Ns \]
This simplifies to:
\[ 50000 = 125 \times Ns \]

### Step 6: Solve for Ns
Now, divide both sides by 125:
\[ Ns = \frac{50000}{125} = 400 \]

### Conclusion
The number of turns required in the secondary coil (Ns) is **400 turns**.

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