Math  /  Algebra

Question27. A star-connected load consists of three identical coils each of resistance 30Ω30 \Omega and inductance 127.3 mH .
If the line current is 5,08 A5,08 \mathrm{~A}, calculate the line voltage if the supply frequency is 50 Hz .

Studdy Solution

STEP 1

1. The load is star-connected.
2. Each coil has a resistance of 30Ω30 \, \Omega and an inductance of 127.3mH127.3 \, \text{mH}.
3. The line current is 5.08A5.08 \, \text{A}.
4. The supply frequency is 50Hz50 \, \text{Hz}.
5. We are to calculate the line voltage.

STEP 2

1. Calculate the impedance of one coil.
2. Calculate the phase voltage using Ohm's Law.
3. Calculate the line voltage from the phase voltage.

STEP 3

Calculate the impedance of one coil.
The impedance Z Z of a coil is given by:
Z=R2+(XL)2 Z = \sqrt{R^2 + (X_L)^2}
where R=30Ω R = 30 \, \Omega is the resistance, and XL X_L is the inductive reactance.
First, calculate the inductive reactance XL X_L :
XL=2πfL X_L = 2 \pi f L
where f=50Hz f = 50 \, \text{Hz} and L=127.3mH=0.1273H L = 127.3 \, \text{mH} = 0.1273 \, \text{H} .
XL=2π×50×0.1273 X_L = 2 \pi \times 50 \times 0.1273
XL40Ω X_L \approx 40 \, \Omega
Now calculate the impedance Z Z :
Z=302+402 Z = \sqrt{30^2 + 40^2}
Z=900+1600 Z = \sqrt{900 + 1600}
Z=2500 Z = \sqrt{2500}
Z=50Ω Z = 50 \, \Omega

STEP 4

Calculate the phase voltage using Ohm's Law.
The phase voltage Vp V_p is given by:
Vp=I×Z V_p = I \times Z
where I=5.08A I = 5.08 \, \text{A} .
Vp=5.08×50 V_p = 5.08 \times 50
Vp=254V V_p = 254 \, \text{V}

STEP 5

Calculate the line voltage from the phase voltage.
For a star connection, the line voltage VL V_L is related to the phase voltage Vp V_p by:
VL=3×Vp V_L = \sqrt{3} \times V_p
VL=3×254 V_L = \sqrt{3} \times 254
VL1.732×254 V_L \approx 1.732 \times 254
VL440V V_L \approx 440 \, \text{V}
The line voltage is:
440V \boxed{440 \, \text{V}}

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