Question

Three identical coils, each of resistance 15 Ω and inductance 42 mH are
connected (a) in star and (b) in delta to a 415 V, 50 Hz, 3-phase supply.
Determine the total power dissipated in each case.

Answer 1

(a) Star connection

Inductive reactance

$X_L = 2πfL \\ X_L = 2π \times 50 \times 42 \times 10^{-3} = 13.19 \;Ω$

Phase impedance

$Z_{ph} = \sqrt{R^2 + X_L^2} \\ Z_{ph} = \sqrt{15^2 + 13.19^2} = 19.97$

Line voltage

$V_{line} = \sqrt{3}V_{ph} \\ V_{ph} = \frac{V_{line}}{\sqrt{3}} = \frac{415}{\sqrt{3}} = 240 \;volts$

Phase current

$I_{ph } = \frac{V_{ph}}{Z_{ph}} \\ I_{ph} = \frac{240}{19.97} = 12.02 \;A$

Line current

$I_{line} = I_{ph} = 12.02 \;A$

Dissipated power

$P = 3I_{line}^2R \\ P = 3 \times (12.02)^2 \times 15 = 6.6 \;kW$

(b) Delta connection

$V_{line} = V_{ph} = 415 \;V \\ Z_{ph} = 19.97 \\ I_{ph} = \frac{V_{ph}}{Z_{ph}} \\ I_{ph} = \frac{415}{19.97} = 20.78 \;A$

Dissipated power

$P = \sqrt{3}I_{ph}^2R \\ P = \sqrt{3} \times 20.78^2 \times 15 = 11.22 \;kW$