# Why does line current equals the total apparent power divided by 3 times the phase voltage?

In this circuit with frequency of 50hz and line to line voltage of 400 V why is the current $I_A = S_t/3V_P$ I don't understand the logic behind since there is one Delta connection, I understand why that formula works for a Star connection but don't for the total of this circuit. The Delta load also has 12,5kw.

• Is $S$ your apparent power? I'm trying to understand your notation. – KingDuken Jun 27 '18 at 20:22
• @KingDuken it is the total apparent power of the three loads, and Vp = 400/sqrt(3) =230 – Pedro Jun 27 '18 at 20:23

$$S_{total} = S_{Z}+S_{c}+S_{equil}$$
$$S = 3 V_{phase} I$$
$$I = \frac{S_{total}}{3V_{phase}}$$