An inductive coil connected to a 200 V, 50 Hz supply takes a current of 10 A. If the power dissipated in the coil is 1000 W. Calculate - a) Inductance of coil b) Power factor c) Angle of lag

 

Given data:

 Supply voltage = 200 V,

 Frequency, f = 50 Hz

 Current = 10 A,

Power, P=1000 W

To find:

 Inductance, L = ?

Power factor, Cos Φ = ?

Angle of lag, Φ = ?

 Solution:

𝐖𝐞 𝐡𝐚𝐯𝐞 𝐈𝐦𝐩𝐞𝐝𝐚𝐧𝐜𝐞, 𝐙 = 𝐕/ 𝐈 = 𝟐𝟎𝟎 /𝟏𝟎 = 𝟐𝟎 Ω

𝐑𝐞𝐬𝐢𝐬𝐭𝐚𝐧𝐜𝐞,𝐑 = 𝐏/ 𝐈^𝟐 = 𝟏𝟎𝟎𝟎 /𝟏𝟎^𝟐 = 𝟏𝟎 Ω

𝐈𝐧𝐝𝐮𝐜𝐭𝐢𝐯𝐞 𝐑𝐞𝐚𝐜𝐭𝐚𝐧𝐜𝐞, 𝐗_𝐋 = √𝐙 ^𝟐 − 𝐑^𝟐 = √𝟐𝟎^𝟐 − 𝟏𝟎^𝟐 = 𝟏𝟕. 𝟑𝟐 Ω

 𝐈𝐧𝐝𝐮𝐜𝐭𝐚𝐧𝐜𝐞, 𝐋 = 𝐗_𝐋/ 𝟐𝛑𝐟 = 𝟏𝟕. 𝟑𝟐 /𝟐𝛑 × 𝟓𝟎 = 𝟎. 𝟎𝟓𝟓 𝐇

 𝐏𝐨𝐰𝐞𝐫 𝐟𝐚𝐜𝐭𝐨𝐫, 𝐂𝐨𝐬Ф = 𝐑/ 𝐙 = 𝟏𝟎/ 𝟐𝟎 = 𝟎. 𝟓 𝐋𝐚𝐠𝐠𝐢𝐧𝐠

 𝐏𝐡𝐚𝐬𝐞 𝐚𝐧𝐠𝐥𝐞, Ф = 𝐂𝐨𝐬^−𝟏 (𝟎. 𝟓) = 𝟔𝟎° 𝐋𝐚g