200 V AC is applied to primary coil of a transformer and it is found that output current is 8 A and output voltage is 50 V. Assume no energy loss. Find the current in primary coil I ampere.

Explanation

To solve the problem, we will use the principle of conservation of energy in a transformer, which states that the power input to the primary coil is equal to the power output from the secondary coil when there are no losses.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Primary Voltage (V1) = 200 V
- Secondary Voltage (V2) = 50 V
- Secondary Current (I2) = 8 A

2. **Write the Power Equations:**
- The power input to the primary coil (P1) can be expressed as:
\[ P_1 = V_1 \times I_1 \]
- The power output from the secondary coil (P2) can be expressed as:
\[ P_2 = V_2 \times I_2 \]

3. **Set the Powers Equal:**
- Since there is no energy loss, we set the input power equal to the output power:
\[ P_1 = P_2 \]
- Therefore, we have:
\[ V_1 \times I_1 = V_2 \times I_2 \]

4. **Rearrange to Find Primary Current (I1):**
- We can rearrange the equation to solve for the primary current (I1):
\[ I_1 = \frac{V_2 \times I_2}{V_1} \]

5. **Substitute the Known Values:**
- Substitute the known values into the equation:
\[ I_1 = \frac{50 \, \text{V} \times 8 \, \text{A}}{200 \, \text{V}} \]

6. **Calculate I1:**
- Perform the multiplication and division:
\[ I_1 = \frac{400}{200} = 2 \, \text{A} \]

7. **Final Result:**
- The current in the primary coil (I1) is 2 A.

### Summary:
The current in the primary coil is **2 A**.