A balanced three phase star connected load of 18 kilo watt taking a leading current of 60 A when connected across a 3 phase 440V, 50Hz supply. Find the values and nature of the load

To find the values and nature of the load, we need to calculate the power factor, impedance, resistance, and reactance.

1. Power Factor Calculation: The total power P (in kW) in a 3 phase load is given by the formula: P = √3 * V * I * cos(θ), where V is the line voltage, I is the line current, and cos(θ) is the power factor. We can rearrange this formula to solve for the power factor: cos(θ) = P / (√3 * V * I). Substituting the given values: cos(θ) = 18 / (√3 * 440 * 60) = 0.95. Since the current is leading, the load is inductive, and the power factor is lagging.

2. Impedance Calculation: The impedance Z (in ohms) of the load is given by the formula: Z = V / I, where V is the phase voltage and I is the phase current. In a star connected system, the phase voltage V = V_line / √3 = 440 / √3 = 254 V. The phase current I = I_line = 60 A. Substituting these values into the formula: Z = 254 / 60 = 4.23 ohms.

3. Resistance Calculation: The resistance R (in ohms) of the load is given by the formula: R = Z * cos(θ), where Z is the impedance and cos(θ) is the power factor. Substituting the calculated values: R = 4.23 * 0.95 = 4.02 ohms.

4. Reactance Calculation: The reactance X (in ohms) of the load is given by the formula: X = Z * sin(θ), where Z is the impedance and sin(θ) is the square root of (1 - cos²(θ)). Substituting the calculated values: X = 4.23 * √(1 - 0.95²) = 0.85 ohms.

So, the load has a power factor of 0.95 lagging, an impedance of 4.23 ohms, a resistance of 4.02 ohms, and a reactance of 0.85 ohms. The nature of the load is inductive because the current is leading.