Three similar coils are star connected to a three phase, 400 V, 50 Hz supply. If the inductance and resistance of each coil are 38.2 mH and 16 Ω respectively. Determine - a) Line current b) Power factor c) Power consumed

 

Given data:

STAR connection, Resistance, R = 16 Ω,

Inductance, L = 𝟑𝟖. 𝟐 × 𝟏𝟎^−𝟑 𝐇 ,

 Line voltage, V_L = 400 V,

 Frequency, f = 50 Hz

To find:

 Line current, I_L = ?

 Power factor, Cos Φ = ?

Power consumed, P = ?

Solution:

 𝐖𝐞 𝐡𝐚𝐯𝐞 𝐈𝐧𝐝𝐮𝐜𝐭𝐢𝐯𝐞 𝐑𝐞𝐚𝐜𝐭𝐚𝐧𝐜𝐞, 𝐗_𝐋 = 𝟐𝛑𝐟𝐋 = 𝟐𝛑 × 𝟓𝟎 × 𝟑𝟖. 𝟐 × 𝟏𝟎^−𝟑 = 𝟏𝟐 Ω

𝐈𝐦𝐩𝐞𝐝𝐚𝐧𝐜𝐞, 𝐙 = √𝐑^𝟐 + 𝐗_𝐋^𝟐 = √𝟏𝟔^𝟐 + 𝟏𝟐^𝟐 = 𝟐𝟎 Ω

 𝐏𝐡𝐚𝐬𝐞 𝐕𝐨𝐥𝐭𝐚𝐠𝐞, 𝐕_𝐏𝐡 = 𝐕_𝐋 /√𝟑 = 𝟒𝟎𝟎/ √𝟑 = 𝟐𝟑𝟏 𝐕

 𝐏𝐡𝐚𝐬𝐞 𝐂𝐮𝐫𝐫𝐞𝐧𝐭,𝐈_𝐏𝐡 = 𝐕_𝐏𝐡 /𝐙_𝐏𝐡 = 𝟐𝟑𝟏/𝟐𝟎 = 𝟏𝟏. 𝟓𝟓 𝐀

 𝐈𝐧 𝐚 𝐬𝐭𝐚𝐫 𝐜𝐨𝐧𝐧𝐞𝐜𝐭𝐞𝐝 𝐬𝐲𝐬𝐭𝐞𝐦,𝐈_𝐏𝐡 = 𝐈_𝐋                                                 ∴ 𝐈𝐋 = 𝟏𝟏. 𝟓𝟓 𝐀

 𝐏𝐨𝐰𝐞𝐫 𝐟𝐚𝐜𝐭𝐨𝐫, 𝐂𝐨𝐬Ф = 𝐑_𝐏𝐡 /𝐙_𝐏𝐡 = 𝟏𝟔 /𝟐𝟎 = 𝟎. 𝟖 𝐋𝐚𝐠𝐠𝐢𝐧𝐠

 𝐏𝐨𝐰𝐞𝐫,𝐏 = 𝟑 𝐕_𝐏𝐡𝐈_𝐏𝐡𝐂𝐨𝐬 𝚽 = 𝟑 × 𝟐𝟑𝟏 × 𝟏𝟏. 𝟓𝟓 × 𝟎. 𝟖 = 𝟔𝟒𝟎𝟎W