A transformer has a turns ratio of 800/200. When its load current is 80A at a power factor of 0.8 lagging, the primary current is 25A lagging at a power factor of 0.707 lagging. Determine the no-load.

To determine the no-load current of the transformer, we can use the following formula:

\[
\text{No-load current} = \sqrt{(I_{\text{primary}}^2 - I_{\text{load}}^2)}
\]

Given:
- Turns ratio = 800/200 = 4
- Load current = 80A at a power factor of 0.8 lagging
- Primary current = 25A lagging at a power factor of 0.707 lagging

First, we need to calculate the apparent power of the load using the load current and power factor:

\[
S_{\text{load}} = V_{\text{load}} \times I_{\text{load}} = 200V \times 80A = 16000VA
\]

Next, we can calculate the apparent power of the primary using the primary current and power factor:

\[
S_{\text{primary}} = V_{\text{primary}} \times I_{\text{primary}} = 800V \times 25A = 20000VA
\]

Now, we can calculate the apparent power of the no-load current using the apparent powers of the load and primary:

\[
S_{\text{no-load}} = S_{\text{primary}} - S_{\text{load}} = 20000VA - 16000VA = 4000VA
\]

Finally, we can calculate the no-load current using the formula mentioned above:

\[
\text{No-load current} = \sqrt{(I_{\text{primary}}^2 - I_{\text{load}}^2)} = \sqrt{(25^2 - 80^2)} = \sqrt{(625 - 6400)} = \sqrt{5775} \approx 75.99A
\]

Therefore, the no-load current of the transformer is approximately 75.99A.

Sure, here is how to determine the no-load current of a transformer given the turns ratio, load current, power factor, and primary current:

Given:

- Turns ratio (N) = 800/200 = 4
- Load current (IL) = 80 A
- Load power factor (pfL) = 0.8 lagging
- Primary current (IP) = 25 A
- Primary power factor (pfP) = 0.707 lagging

Solution:

1. Calculate the load apparent power (SL):

```
SL = IL - VL - pfL
```

where VL is the load voltage.

Since the turns ratio is 4, the load voltage is 1/4 of the primary voltage. Therefore,

```
VL = VP / 4
```

Substituting this into the equation for SL, we get:

```
SL = IL - (VP / 4) - pfL
```

```
SL = 80 A - (VP / 4) - 0.8
```

```
SL = 16 VP VA
```

2. Calculate the primary apparent power (SP):

```
SP = IP - VP - pfP
```

```
SP = 25 A - VP - 0.707
```

```
SP = 17.675 VP VA
```

3. Equate the apparent powers and solve for VP:

```
SL = SP
```

```
16 VP = 17.675 VP
```

```
VP = 1.105 V
```

4. Calculate the no-load current (IN):

```
IN = IP - (IL / N)
```

```
IN = 25 A - (80 A / 4)
```

```
IN = 5 A
```

Therefore, the no-load current of the transformer is 5 A.