To calculate the number of turns per limb on both the high-voltage (HV) and low-voltage (LV) sides of the transformer, we need to apply some basic transformer design principles, particularly the equation that relates flux, voltage, frequency, and number of turns.

Given Data:

• Core dimensions: 20 cm x 20 cm (side of square core)
• Permissible maximum flux density (B) = 1 Wb/m²
• Frequency (f) = 50 Hz
• Voltage ratio (V_HV / V_LV) = 300 V / 220 V
• Core area (A) = 20 cm × 20 cm = $(0.2 \, \text{m})^2 = 0.04 \, \text{m}^2$

Step 1: Calculate the Flux (Φ)

The maximum magnetic flux (Φ) is related to the flux density (B) and the cross-sectional area (A) of the core:

$\Phi = B \times A$

Substitute the known values:

$\Phi = 1 \, \text{Wb/m}^2 \times 0.04 \, \text{m}^2 = 0.04 \, \text{Wb}$

Step 2: Calculate the Number of Turns (N) on Each Side

The number of turns $N$ is given by the formula for the transformer:

$V = 4.44 \times f \times N \times \Phi$

Where:

• $V$ is the voltage (on either side),
• $f$ is the frequency,
• $N$ is the number of turns per phase on the respective side,
• $\Phi$ is the maximum flux.

We will solve for $N$ (number of turns) for both the HV and LV sides.

High Voltage Side (HV)

For the HV side:

$V_{HV} = 300 \, \text{V}, \quad f = 50 \, \text{Hz}, \quad \Phi = 0.04 \, \text{Wb}$

Rearrange the formula to solve for $N_{HV}$:

$N_{HV} = \frac{V_{HV}}{4.44 \times f \times \Phi}$

Substitute the known values:

$N_{HV} = \frac{300}{4.44 \times 50 \times 0.04}$

$N_{HV} = \frac{300}{8.88}$

$N_{HV} = 33.80 \approx 34 \, \text{turns}$

Low Voltage Side (LV)

For the LV side:

$V_{LV} = 220 \, \text{V}, \quad f = 50 \, \text{Hz}, \quad \Phi = 0.04 \, \text{Wb}$

Again, rearrange the formula to solve for $N_{LV}$:

$N_{LV} = \frac{V_{LV}}{4.44 \times f \times \Phi}$

Substitute the known values:

$N_{LV} = \frac{220}{4.44 \times 50 \times 0.04}$

$N_{LV} = \frac{220}{8.88}$

$N_{LV} = 24.77 \approx 25 \, \text{turns}$

Final Answers:

• Number of turns per limb on the high voltage side (HV): $34$ turns
• Number of turns per limb on the low voltage side (LV): $25$ turns

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Would you like further details or clarifications on this calculation? Here are some related questions you may find interesting:

1. How does the flux density impact transformer efficiency?
2. What would happen if the flux density were increased above the permissible limit?
3. How do the turns ratios relate to the voltage ratios in transformers?
4. How is the core area related to the transformer’s power rating?
5. What other factors influence the transformer design aside from voltage and frequency?

Tip: Always ensure that the core material used in transformers can handle the maximum flux density without reaching saturation, as this will affect the performance and efficiency.