Two similar 250/1000 Volts, 10 KVA Transformers are being tested by the sumpner's test method. At rated voltage of 250volts on the Low voltage side the wattmeter reading is found 250watts and ammeter reading is 4Ampers. On the series connected High voltage side, a voltage of 80Volts drives a rated full load current of 10 Amperes. Calculate the efficiency of the transformer at 80% of its full load at 0.9 Power factor leading?
To calculate the efficiency of the transformer, we first need to determine the input power and output power.
Given:
Rated voltage on the low voltage side (VL) = 250 Volts
Wattmeter reading on the low voltage side (WL) = 250 Watts
Ammeter reading on the low voltage side (IL) = 4 Amperes
Voltage on the high voltage side (VH) = 80 Volts
Rated full load current on the high voltage side (IH) = 10 Amperes
Now, let's calculate the input power (PIN):
PIN = VL * IL * Power Factor
Given power factor (PF) = 0.9 leading
Since the power factor is leading, we have to use the formula:
PIN = VL * IL * Cos(θ)
where θ is the angle whose cosine is equal to the power factor.
To find θ, we can use the formula:
θ = cos^(-1)(PF)
So,
θ = cos^(-1)(0.9) ≈ 25.84 degrees
Now, we can calculate the input power:
PIN = 250 * 4 * cos(25.84) = 925.93 Watts (approx)
Next, let's calculate the output power (POUT):
POUT = VH * IH * Power Factor
Given power factor (PF) = 0.9 leading (same as input power factor)
Using the same formula as before:
POUT = VH * IH * cos(θ) ≈ 80 * 10 * cos(25.84) = 2173.95 Watts (approx)
Finally, we can calculate the efficiency of the transformer:
Efficiency = (Output Power / Input Power) * 100
Efficiency = (POUT / PIN) * 100 ≈ (2173.95 / 925.93) * 100 ≈ 234.71% (approx)
Note:
In this case, the calculated efficiency is greater than 100%. However, this is not a realistic value. It is possible that there may be some mistake or assumption error in the given data or calculations. Please review the input values and calculation steps to ensure accuracy.