Calculate phase voltage

Since the line voltage is given as 100 kV, the phase-to-neutral voltage is $V_{ph} = \frac{V_L}{\sqrt{3}} = \frac{10⁵}{\sqrt{3}} \approx 57735 V$.

$V_{ph} = \frac{10⁵}{\sqrt{3}}$

Determine angular frequency

The angular frequency $\omega$ for 50 Hz is calculated as $\omega = 2 \pi f$.

$\omega = 2 \times \pi \times 50 = 314.16 \text{ rad/s}$

Calculate charging current

Substitute the values into the charging current formula: $I_{ch} = V_{ph} \times \omega \times C_n$.

$I_{ch} = \frac{10⁵}{\sqrt{3}} \times 314.16 \times 0.01 \times 10^{-6}$

Final Result

Performing the arithmetic calculation: $I_{ch} \approx 57735 \times 3.1416 \times 10^{-6} \approx 0.1814 A/km$.

$I_{ch} \approx 181 \times 10^{-3} \text{ A/km}$