Question

(a) Derive the expression for current and voltage relations between line and phase values in the star and delta cases. Draw vector diagram. (6)

(b) Three impedances Z = 5 + j4 are connected in the form of a delta to the three loads of a balanced 3-phase circuit. The line voltage is 120 volts. Find (10)

(i) The phase current

(ii) Power factor

(iii) The volt-ampere in the circuit.

Answer 1

(b) Given:

$$\operatorname{Impedance}\:\left(Z\right)=5+j4\:=\:\sqrt{5^2+4^2}$$

$$Voltage\left(V\right)=120V$$

Circuit is connected in Delta, so voltage is same.

$$V_{L}=V_{phase}$$

(i) The phase current:

$$I_{L}=\sqrt3\times I_{ph}$$

$$V=IR$$

$$I_{ph}=\frac{V_{L}}{Z}$$

$$I_{ph}=\frac{120}{\sqrt{5^2}+4^2}$$

$$I_{ph}=\frac{120}{6.4}$$

$$I_{ph}=18.75A$$

(ii) Power factor:

$$\cos\phi=\frac{R}{Z}$$

$$\cos\phi=\frac{5}{6.4}$$

$$\cos\phi=0.78$$

(iii) The volt-ampere in the circuit:

$$=V_{ph}\times I_{ph}$$

$$=120\times18.75$$

$$=2250V$$

✓ Verified Model Answer (Text Solution)