Math Snap

STEP 1

1. The load is star-connected.
2. Each coil has a resistance of $30 \, \Omega$ and an inductance of $127.3 \, \text{mH}$.
3. The line current is $5.08 \, \text{A}$.
4. The supply frequency is $50 \, \text{Hz}$.
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 $Z$ of a coil is given by:
$$Z = \sqrt{R^2 + (X_L)^2}$$ where $R = 30 \, \Omega$ is the resistance, and $X_L$ is the inductive reactance.
First, calculate the inductive reactance $X_L$:
$$X_L = 2 \pi f L$$ where $f = 50 \, \text{Hz}$ and $L = 127.3 \, \text{mH} = 0.1273 \, \text{H}$.
$$X_L = 2 \pi \times 50 \times 0.1273$$ $$X_L \approx 40 \, \Omega$$ Now calculate the impedance $Z$:
$$Z = \sqrt{30^2 + 40^2}$$ $$Z = \sqrt{900 + 1600}$$ $$Z = \sqrt{2500}$$ $$Z = 50 \, \Omega$$

STEP 4

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

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