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`

Explanation

To solve the problem step by step, we will use the principles of transformers and the relationships between power, voltage, and turns in the coils.

### Step 1: Understand the given information
We have:
- Number of turns in the primary coil (Np) = 100 turns
- Current in the primary coil (Ip) = 8 A
- Input power (Pin) = 1 kW = 1000 W
- Output voltage (Vs) = 500 V
- We need to find the number of turns in the secondary coil (Ns).

### 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):
\[ Vp = \frac{P_{in}}{I_p} \]
Substituting the known values:
\[ Vp = \frac{1000 \, \text{W}}{8 \, \text{A}} = 125 \, \text{V} \]

### Step 3: Use the transformer turns ratio
The relationship between the turns in the primary and secondary coils and the voltages is given by:
\[ \frac{N_s}{N_p} = \frac{V_s}{V_p} \]
Rearranging this gives:
\[ N_s = N_p \times \frac{V_s}{V_p} \]

### Step 4: Substitute the values into the equation
Substituting the known values into the equation:
\[ N_s = 100 \times \frac{500 \, \text{V}}{125 \, \text{V}} \]

### Step 5: Calculate the number of turns in the secondary coil (Ns)
Now, we can calculate:
\[ N_s = 100 \times 4 = 400 \]

### Conclusion
The number of turns required in the secondary coil to have an output of 500 V is **400 turns**.

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