A series circuit consists of a non-inductive resistor of 10 Ω, an inductor having a reactance of 50 Ω and a capacitor having a reactance of 30 Ω. It is connected to a 230 V AC supply. Calculate - a) Current b) Power Consumed c) Power factor

 

Given data:

 Resistance, R = 10 Ω,

 Inductive reactance, X_L = 50 Ώ,

 Capacitive reactance, X_C = 30 Ώ,

 Supply voltage, V=230 V

 To find:

 Current, I = ?

 Power, P = ?

Power factor, Cos Φ = ?

 Solution:

 𝐈𝐦𝐩𝐞𝐝𝐚𝐧𝐜𝐞, 𝐙 = √𝐑^𝟐 + (𝐗_𝐋 − 𝐗_𝐂)^𝟐 = √𝟏𝟎^𝟐 + (𝟓𝟎 − 𝟑𝟎) ^𝟐 = 𝟐𝟐. 𝟑𝟔 Ω

 𝐂𝐮𝐫𝐫𝐞𝐧𝐭,𝐈 = 𝐕/ 𝐙 = 𝟐𝟑𝟎/ 𝟐𝟐. 𝟑𝟔 = 𝟏𝟎. 𝟐𝟖 𝐀

𝐏𝐨𝐰𝐞𝐫 𝐜𝐨𝐧𝐬𝐮𝐦𝐞𝐝, 𝐏 = 𝐈^𝟐𝐑 = (𝟏𝟎. 𝟐𝟖) ^𝟐 × 𝟏𝟎 = 𝟏𝟎𝟓𝟕 𝐖

𝐏𝐨𝐰𝐞𝐫 𝐟𝐚𝐜𝐭𝐨𝐫, 𝐂𝐨𝐬Ф = 𝐑 /𝐙 = 𝟏𝟎 /𝟐𝟐. 𝟑𝟔 = 𝟎. 𝟒𝟒𝟕 Lagging