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Introductory Physics Homework Help
Impedance & complex currents & voltages
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[QUOTE="ehild, post: 5788031, member: 481"] The instantaneous power is the product of the real voltage and the real current. The complex form of power and voltage can be used for linear operations only (addition, multiplication with constant). In general, the current and voltage need not be in phase. The complex voltage [B][I]U[/I][/B] and complex current[B][I] I[/I][/B] are related through the complex impedance [I][B]Z=[/B][/I]Ze[SUP]iφ[/SUP]: [B][I]U[/I][/B][I]=[/I][B][I]ZI. [/I][/B]Writing in the Euler form, [B][I]I[/I][/B]=I[SUB]0[/SUB]e[SUP]iωt[/SUP], [I][B]U[/B][/I][B]=[/B][I][B]ZI[/B][/I]=I[SUB]0[/SUB]Z e[SUP]i(ωt+φ)[/SUP]=U[SUB]0[/SUB]e[SUP]i(ωt+φ)[/SUP]. The instantaneous power is the product or the real part of the complex current (I(t)=I[SUB]0[/SUB]cos(ωt) with the real part of the complex voltage U(t)=U[SUB]0[/SUB]cos(ωt+φ)), where U[SUB]0[/SUB]=I[SUB]0[/SUB]Z. The problem asks the average power, so you integrate the instantaneous power for a period and divide by the period T. [/QUOTE]
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Impedance & complex currents & voltages
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