Question27. A star-connected load consists of three identical coils each of resistance $30 \Omega$ and inductance 127.3 mH . If the line current is $5,08 \mathrm{~A}$, calculate the line voltage if the supply frequency is 50 Hz .
Ans. 440V.
28. Three identical coils each of resistance $30 \Omega$ and inductance $127,3 \mathrm{mH}$ are connected in delta to a 440 V , 50 Hz , 3-phase supply. Determine (a) the phase current, and (b) the line current.
Ans. a) 8,8 A; b) $15,24 \mathrm{~A}$

STEP 1

1. The load is a balanced three-phase system.
2. The coils have a resistance of $30 \, \Omega$ and an inductance of $127.3 \, \text{mH}$.
3. The supply frequency is $50 \, \text{Hz}$.
4. For the star connection, the line current is $5.08 \, \text{A}$.
5. For the delta connection, the line voltage is $440 \, \text{V}$.
_HIGH_LEVEL_APPROACH_ for Problem 27:
1. Calculate the impedance of each coil.
2. Calculate the phase voltage for the star connection.
3. Calculate the line voltage for the star connection.
_HIGH_LEVEL_APPROACH_ for Problem 28:
1. Calculate the impedance of each coil.
2. Calculate the phase current for the delta connection.
3. Calculate the line current for the delta connection.
Problem 27:

STEP 2

STEP 3

Calculate the impedance of each coil:
$$Z = \sqrt{R^2 + (X_L)^2}$$
Where: - $R = 30 \, \Omega$ - $X_L = 2 \pi f L$ - $f = 50 \, \text{Hz}$ - $L = 127.3 \, \text{mH} = 0.1273 \, \text{H}$
Calculate $X_L$:
$$X_L = 2 \pi \times 50 \times 0.1273 = 40 \, \Omega$$
Calculate $Z$:
$$Z = \sqrt{30^2 + 40^2} = \sqrt{900 + 1600} = \sqrt{2500} = 50 \, \Omega$$

STEP 4

Calculate the phase voltage for the star connection:
$$V_{\text{phase}} = I_{\text{line}} \times Z$$ $$V_{\text{phase}} = 5.08 \, \text{A} \times 50 \, \Omega = 254 \, \text{V}$$

STEP 5

Calculate the line voltage for the star connection:
$$V_{\text{line}} = \sqrt{3} \times V_{\text{phase}}$$ $$V_{\text{line}} = \sqrt{3} \times 254 \, \text{V} \approx 440 \, \text{V}$$
Problem 28:
STEP_1: Calculate the impedance of each coil (already calculated in Problem 27):
$$Z = 50 \, \Omega$$
STEP_2: Calculate the phase current for the delta connection:
$$V_{\text{phase}} = V_{\text{line}} = 440 \, \text{V}$$ $$I_{\text{phase}} = \frac{V_{\text{phase}}}{Z}$$ $$I_{\text{phase}} = \frac{440 \, \text{V}}{50 \, \Omega} = 8.8 \, \text{A}$$
STEP_3: Calculate the line current for the delta connection:
$$I_{\text{line}} = \sqrt{3} \times I_{\text{phase}}$$ $$I_{\text{line}} = \sqrt{3} \times 8.8 \, \text{A} \approx 15.24 \, \text{A}$$
The answers are: - Problem 27: Line voltage is $\boxed{440 \, \text{V}}$. - Problem 28: (a) Phase current is $\boxed{8.8 \, \text{A}}$; (b) Line current is $\boxed{15.24 \, \text{A}}$.