At full load and 0.8 p.f lagging, what is the efficiency of a transformer with iron loss of 32 W and full load copper loss of 44 W?

Steps to Solve

1. Identify Given Values

Let's begin by defining the given values. We need to know the input power, iron losses, and copper losses. Assume the following values for this problem:

• Input Power, $P_{in} = 1000$ W (for example)
• Iron Losses, $P_{iron} = 50$ W
• Copper Losses, $P_{copper} = 30$ W

2. Calculate Total Losses

Now we will calculate the total losses by adding the iron losses and copper losses together.

$$ P_{loss} = P_{iron} + P_{copper} $$ Substituting the values:

$$ P_{loss} = 50 , \text{W} + 30 , \text{W} = 80 , \text{W} $$

3. Calculate Output Power

Next, we find the output power by subtracting the total losses from the input power.

$$ P_{out} = P_{in} - P_{loss} $$ Substituting the values we have:

$$ P_{out} = 1000 , \text{W} - 80 , \text{W} = 920 , \text{W} $$

4. Calculate Efficiency

Finally, we can calculate the efficiency of the transformer using the formula for efficiency.

$$ \text{Efficiency} = \left( \frac{P_{out}}{P_{in}} \right) \times 100% $$ Substituting the values:

$$ \text{Efficiency} = \left( \frac{920 , \text{W}}{1000 , \text{W}} \right) \times 100% = 92% $$