A circuit is made up of 5 Ω resistance, 0.2 H inductance and 60 μF capacitance in series. If the circuit current is 20 A at a supply frequency of 50 Hz. Find the applied voltage?

 

Given data:

 Resistance, R = 5 Ω,

 Inductance, L = 0.2 H,

 Capacitance, C = 120 μF,

 Current, I = 20 A

 Supply frequency, f=50 Hz

To find:

 Supply voltage, V = ?

 Solution:

𝐖𝐞 𝐡𝐚𝐯𝐞 𝐈𝐧𝐝𝐮𝐜𝐭𝐢𝐯𝐞 𝐑𝐞𝐚𝐜𝐭𝐚𝐧𝐜𝐞, 𝐗_𝐋 = 𝟐𝛑𝐟𝐋 = 𝟐𝛑 × 𝟓𝟎 × 𝟎. 𝟐 = 𝟔𝟐. 𝟖𝟑 Ω

𝐂𝐚𝐩𝐚𝐜𝐢𝐭𝐢𝐯𝐞 𝐑𝐞𝐚𝐜𝐭𝐚𝐧𝐜𝐞, 𝐗_𝐂 = 𝟏/ 𝟐𝛑𝐟𝐂 = 𝟏/ 𝟐𝛑 × 𝟓𝟎 × 𝟔𝟎 × 𝟏𝟎^−𝟔 = 𝟓𝟑. 𝟎𝟓 Ω

 𝐈𝐦𝐩𝐞𝐝𝐚𝐧𝐜𝐞, 𝐙 = √𝐑^𝟐 + (𝐗_𝐋 − 𝐗_𝐂) ^𝟐 = √𝟓 ^𝟐 + (𝟔𝟐. 𝟖𝟑 − 𝟓𝟑. 𝟎𝟓)^𝟐 = 𝟏𝟎. 𝟗𝟖 Ω

𝐀𝐩𝐩𝐥𝐢𝐞𝐝 𝐕𝐨𝐥𝐭𝐚𝐠𝐞, 𝐕 = 𝐈 𝐙 = 𝟐𝟎 × 𝟏𝟎. 𝟗𝟖 = 𝟐𝟏𝟗 𝐕