To determine the capacitance per kilometer for a singlephase overhead line with the given parameters we can use the formula for the capacitance per unit length of a pair of parallel wires C frac2pi varepsilon0lnleftfracdrright Where C capacitance per unit length Fm varepsilon0 permittivity of free space 8854 times 1012 text Fm d distance between the centers of the two wires m r radius of the wires m Given Diameter of wires 10 mm 001 m hence radius r frac0012 0005 textm Distance between wires d 2 textm Now we can calculate the capacitance per unit length C C frac2 pi 8854 times 1012lnleftfrac20005right Calculating lnleftfrac20005right frac20005 400 quad Rightarrow quad ln400 approx 5991 Now plug this back into the capacitance formula C frac2 pi 8854 times 10125991 Calculating C C approx frac2 times 31416 times 8854 times 10125991 approx 935 times 1012 text Fm To express this in terms of capacitance per kilometer Ckm C times 1000 approx 935 times 1012 times 1000 approx 935 times 109 text Fkm Now the charging current Ic can be calculated using the formula Ic C cdot V cdot omega Where Ic charging current A V voltage V omega 2pi f where f is the frequency in Hz Given V 50000 textV and f 50 textHz omega 2pi 50 approx 31416 textrads Now substituting C converted to Fkm for the entire line length 30 km C30 km 935 times 109 text Fkm times 30 text km 2805 times 107 text F Now calculating Ic Ic 2805 times 107 cdot 50000 cdot 31416 Calculating Ic Ic approx 2805 times 107 times 50000 times 31416 approx 44 textA The final answers are Ckm approx 935 textnFkm Ic approx 44 textA Here are the final values in a convenient format plaintext Capacitance per km 935 nFkm Charging current 44 A If you have any further questions or need clarification feel free to ask You can also try out the Homeworkify Mobile App for an improved experience Homeworkify Apphttpshomeworkifycomcohomeworkifyapp