. A 200 V, 50 Hz, inductive circuit takes a current of 10 A lagging the voltage by 30°. Calculate - a) Resistance b) Reactance c) Inductance of the circuit

 

Given data:

Supply voltage = 200 V,

 Frequency, f = 50 Hz,

Current = 10 A,

 Phase angle, Φ=30° Lag

 To find: Resistance, R = ?

Inductive Reactance, X_L = ?

Inductance, L = ?

Solution:

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

 𝐑𝐞𝐬𝐢𝐬𝐭𝐚𝐧𝐜𝐞, 𝐑 = 𝐙 𝐂𝐨𝐬Ф = 𝟐𝟎 𝐂𝐨𝐬 𝟑𝟎° = 𝟐𝟎 × 𝟎. 𝟖𝟔𝟔 = 𝟏𝟕. 𝟑𝟐 Ω

 𝐈𝐧𝐝𝐮𝐜𝐭𝐢𝐯𝐞 𝐑𝐞𝐚𝐜𝐭𝐚𝐧𝐜𝐞, 𝐗_𝐋 = 𝐙 𝐒𝐢𝐧Ф = 𝟐𝟎 𝐒𝐢𝐧 𝟑𝟎° = 𝟐𝟎 × 𝟎. 𝟓 = 𝟏𝟎 Ω

 𝐈𝐧𝐝𝐮𝐜𝐭𝐚𝐧𝐜𝐞, 𝐋 = 𝐗_𝐋 /𝟐𝛑𝐟 = 𝟏𝟎/ 𝟐𝛑 × 𝟓𝟎 = 𝟎. 𝟎𝟑𝟏𝟖 H