Calculating the Number of Turns in the Primary Winding of a Transformer:

In order to calculate the number of turns in the primary winding of a transformer, we need to use the given information about the no load current, power factor, and supply voltage.

Given:
- No load current (Io) = 15A
- Power factor (PF) = 0.2
- Supply voltage (V) = 460V
- Frequency (f) = 50Hz

Formula:
The no load current of a transformer can be determined using the following formula:

Io = (Vp / √3) * (Ip / Np)

Where:
- Io is the no load current
- Vp is the primary voltage
- Ip is the primary current
- Np is the number of turns in the primary winding

We can rearrange the formula to solve for Np:

Np = (Vp / √3) * (Ip / Io)

Calculating the Number of Turns:
To calculate the number of turns in the primary winding (Np), we need to determine the primary current (Ip). We can use the power factor to calculate the primary current.

Calculating Primary Current (Ip):
The power factor (PF) can be calculated using the formula:

PF = P / (Vp * Ip)

Where:
- P is the real power
- Vp is the primary voltage
- Ip is the primary current

We can rearrange the formula to solve for Ip:

Ip = P / (Vp * PF)

Calculating Real Power (P):
The real power (P) can be calculated using the formula:

P = √3 * Vp * Ip * PF

Substituting Values:
Now, we can substitute the given values into the formulas to calculate the primary current (Ip), real power (P), and ultimately the number of turns in the primary winding (Np).

1. Calculate Primary Current (Ip):
Ip = P / (Vp * PF)
Ip = (√3 * Vp * Ip * PF) / (Vp * PF)
Ip = √3 * Ip

2. Calculate Real Power (P):
P = √3 * Vp * Ip * PF
P = √3 * 460V * Ip * 0.2
P = √3 * 460V * Ip * 0.2

3. Substitute Values into the Number of Turns Formula:
Np = (Vp / √3) * (Ip / Io)
Np = (460V / √3) * (Ip / 15A)

By substituting the calculated values of Ip and solving the equation, we can determine the number of turns in the primary winding (Np).