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Parallel Rlc Circuit

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Running Head: PARALLEL RLC CIRCUIT 1 Parallel RLC Circuit Name: Institution: Instructor: Date: PARALLEL RLC CIRCUIT 2 Parallel RLC Circuit Question 1 Consider the parallel RLC Circuit below: Analyze the RLC circuit to determine the following (include both polar and complex forms where applicable): Solution ω = 2πf = 2π × 79.577 = 500 rad per second V1 = 20 < 300 V Impendence of the capacitor Rx = 1 1 = = −j8Ω jωC j(500)(0.25 × 10−3 ) Impendence of the inductor R L = jωL = j(500)(4 × 10−3 ) = j2Ω R = 8Ω Xc = −8j XL = 2j a) 𝐙𝐞𝐪 1 1 1 1 = + + Zeq R Xc X L 1 1 1 1 = − + = 0.125 + 0.125j − 0.5j = 0.125 − 0.375j Zeq 8 8j 2j Zeq = 1 (0.125 + 0.375j) 0.125 + 0.375j × = = 0.8 + 2.4j 0.125 − 0.375j (0.125 + 0.375j) 0.15625 PARALLEL RLC CIRCUIT 3 𝐀𝐧𝐬𝐰𝐞𝐫 𝐙𝐞𝐪 = 𝟎. 𝟖 + 𝟐. 𝟒𝐣𝛀 𝐨𝐫 𝐙𝐞𝐪 = 𝟐. 𝟓𝟐𝟗𝟖 < 𝟕𝟏. 𝟓𝟔𝟓𝟏𝟎 b) The total Current IT = V1 20 < 300 = = 7.906 < −41.5650 A ZT 2.5298 < 71.56510 𝐀𝐧𝐬𝐰𝐞𝐫 𝐈𝐓 = 𝟕. 𝟗𝟎𝟔 < −𝟒𝟏. 𝟓𝟔𝟓𝟎 𝐀 𝐨𝐫 𝐈𝐓 = 𝟓. 𝟗𝟏𝟓𝟑 − 𝐣𝟓. 𝟐𝟒𝟓𝟒 𝐀 c) The current through the resistor IR1 V1 20 < 300 = = = 2.5 < 300 A R 8 < 00 𝐀𝐧𝐬𝐰𝐞𝐫: 𝐈𝐑𝟏 = 𝟐. 𝟓 < 𝟑𝟎𝟎 𝐀 𝐨𝐫 𝐈𝐑𝟏 = 𝟐. 𝟏𝟔𝟓𝟏 + 𝐣𝟏. 𝟐𝟓 d) The current through the inductor IL1 V1 20 < 300 = = = 10 < −60 ...
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