A coil has a resistance of 75 Ω and an inductance of 1.4 H. When the applied AC voltage is 240 V at what frequency will the current be 0.3 A? What is the power factor at this frequency?

 

Given data:

Resistance, R = 75 Ω,

 Inductance, L = 1.4 H,

 Supply voltage = 240 V,

Current, I= 0.3 A

 To find:

Frequency, f = ?

 Power factor, Cos Φ = ?

Solution:

 𝐖𝐞 𝐡𝐚𝐯𝐞 𝐈𝐦𝐩𝐞𝐝𝐚𝐧𝐜𝐞, 𝐙 = 𝐕/ 𝐈 = 𝟐𝟒𝟎/ 𝟎. 𝟑 = 𝟖𝟎𝟎 Ω

 𝐈𝐧𝐝𝐮𝐜𝐭𝐢𝐯𝐞 𝐑𝐞𝐚𝐜𝐭𝐚𝐧𝐜𝐞, 𝐗_𝐋 = √𝐙^𝟐 − 𝐑^𝟐 = √𝟖𝟎𝟎^𝟐 − 𝟕𝟓^𝟐 = 𝟕𝟗𝟔. 𝟓 Ω

 𝐅𝐫𝐞𝐪𝐮𝐞𝐧𝐜𝐲, 𝐟 = 𝐗_𝐋 /𝟐𝛑𝐋 = 𝟕𝟗𝟔. 𝟓/ 𝟐𝛑 × 𝟏. 𝟒 = 𝟗𝟎. 𝟓 𝐇𝐳

 𝐏𝐨𝐰𝐞𝐫 𝐟𝐚𝐜𝐭𝐨𝐫, 𝐂𝐨𝐬Ф = 𝐑/ 𝐙 = 𝟕𝟓 /𝟖𝟎𝟎 = 𝟎. 𝟎𝟗𝟒 𝐋𝐚𝐠𝐠𝐢𝐧𝐠