Determine line current and power absorbed when 3 coils. 6Ω and 8Ω inductive reactance are connected in star and delta across 400V, 3-phase supply.

Steps to Solve

1. Determine Star Configuration Current Use the formula for line current in a star connection: $$ I_L = \frac{V_L}{Z_Y} $$ where ( Z_Y ) is the impedance in the star configuration.

For each coil:

• Resistance, ( R = 6 , \Omega )
• Inductive reactance, ( X_L = 8 , \Omega )

Calculate total impedance: $$ Z_Y = \sqrt{R^2 + X_L^2} = \sqrt{6^2 + 8^2} = \sqrt{100} = 10 , \Omega $$

Now, find the line current: $$ I_L = \frac{400}{10} = 40 , A $$

2. Calculate Power in Star Configuration The total power absorbed in a 3-phase star connection is given by: $$ P_Y = \sqrt{3} \cdot V_L \cdot I_L $$

Substitute ( V_L = 400 , V ) and ( I_L = 40 , A ): $$ P_Y = \sqrt{3} \cdot 400 \cdot 40 $$

Calculate: $$ P_Y \approx 1.732 \cdot 400 \cdot 40 \approx 27,600 , W $$

3. Determine Delta Configuration Current For a delta connection, the line current is: $$ I_L = \frac{V_L}{Z_\Delta} $$ where ( Z_\Delta = \frac{Z_Y}{3} ).

So the impedance in delta is: $$ Z_\Delta = Z_Y = 10 , \Omega $$

Now, calculate line current in delta: $$ I_L = \frac{400}{10} = 40 , A $$

4. Calculate Power in Delta Configuration Use the formula for power in a delta connection: $$ P_\Delta = 3 \cdot V_P \cdot I_P $$

Since ( V_P = V_L ) in delta,

• Phase Voltage ( V_P = \frac{400}{\sqrt{3}} \approx 230.94 , V )
• Current per phase ( I_P = I_L )

Substituting values: $$ P_\Delta = 3 \cdot 230.94 \cdot 40 $$

Calculate: $$ P_\Delta \approx 27,600 , W $$