To solve for the value of the inductances in each phase, let's go through the given data and the necessary steps to find it.

Given Data:

• Supply Voltage (Line Voltage), $V_L = 400 \text{ V}$
• Frequency, $f = 60 \text{ Hz}$
• Total Power, $P = 15 \text{ kW} = 15000 \text{ W}$
• Phase Resistance, $R = 10 \, \Omega$

Since this is a balanced star-connected load:

1. The line voltage $V_L$ and the phase voltage $V_{ph}$ are related by: $V_{ph} = \frac{V_L}{\sqrt{3}}$

2. The total power for a 3-phase system is given by: $P = 3 \times V_{ph} \times I_{ph} \times \cos \phi$ where:

   • $I_{ph}$ is the phase current
   • $\cos \phi$ is the power factor

3. The impedance $Z$ in each phase, considering resistance $R$ and inductive reactance $X_L$, can be expressed as: $Z = \sqrt{R^2 + X_L^2}$ where $X_L = 2 \pi f L$ and $L$ is the inductance.

Steps to Solve:

1. Calculate Phase Voltage $V_{ph}$: $V_{ph} = \frac{400}{\sqrt{3}} = 230.94 \, \text{V}$

2. Determine Phase Current $I_{ph}$ Using Power:

   The total power in terms of phase voltage and current is: $15000 = 3 \times V_{ph} \times I_{ph} \times \cos \phi$ Rearranging to solve for $I_{ph} \cdot \cos \phi$: $I_{ph} \cdot \cos \phi = \frac{15000}{3 \times 230.94} = 21.65 \, \text{A}$

3. Calculate Impedance $Z$:

   The phase current is also given by: $I_{ph} = \frac{V_{ph}}{Z}$ Since $\cos \phi = \frac{R}{Z}$: $Z = \frac{R}{\cos \phi}$

4. Determine Inductance $L$: