A 10 kVA, 2000/400 V single-phase transformer has a primary resistance...
Ω and 10 Ω respectively. The secondary resistance and inductive reactance are 0.05 Ω and 0.1 Ω respectively. The transformer is operating at full load with a power factor of 0.8 lagging. Calculate the primary and secondary currents, as well as the power factor seen by the primary and secondary windings.
To calculate the primary and secondary currents, we can use the formula:
I = S / V
Where I is the current, S is the apparent power, and V is the voltage.
For the primary current, the apparent power is 10 kVA and the voltage is 2000 V:
I_primary = 10 kVA / 2000 V = 5 A
For the secondary current, the apparent power is also 10 kVA, but the voltage is 400 V:
I_secondary = 10 kVA / 400 V = 25 A
Next, let's calculate the power factor seen by the primary and secondary windings.
The power factor is given by the formula:
power factor = cos(θ)
Where θ is the phase angle between the current and voltage.
For the primary power factor, the power factor is given as 0.8 lagging, so θ_primary = cos^(-1)(0.8) = 36.87 degrees.
For the secondary power factor, we can use the formula:
tan(θ_secondary) = X_secondary / R_secondary
Where X_secondary is the secondary inductive reactance and R_secondary is the secondary resistance.
θ_secondary = tan^(-1)(0.1 Ω / 0.05 Ω) = 63.43 degrees.
Finally, let's calculate the power factor seen by the primary and secondary windings using the formula:
power factor = cos(θ)
For the primary power factor:
power factor_primary = cos(36.87 degrees) = 0.8
For the secondary power factor:
power factor_secondary = cos(63.43 degrees) = 0.45
Therefore, the primary current is 5 A, the secondary current is 25 A, the power factor seen by the primary winding is 0.8, and the power factor seen by the secondary winding is 0.45.