please show steps-by-steps solutions tq 3. Aside from the typical RLC circuit arranged in series, there exist that arranged in parallelas well (see Figure 3). In this configuration, the instantaneous voltages (and rms voltages)across each of the three circuit elements are the same, and each is in phase with the currentin the resistor. The currents in C and L lead or lag the current in the resistor as shown inthe phasor diagram (Figure 3b). By taking the instantaneous voltage across the AC sourcesin ot and the instantaneous current provided by the AC source to beto be v(t)=V,ampi(t) = 1mp sin (ot – ø) , where Vmp and Imp are the voltage and current amplitudes%3Damprespectively,(a)(b)AVIcR.|AV.rmsRFigure 3: (a) RLC circuit in parallel configuration and (b) phasor diagram for the RLC circuit.(a). Write the instantaneous currents across the three circuit elements in terms ofV.amp >angular frequency @, inductance L, and capacitance C.(b). Relate for the ratio of the rms voltage and current towards the ratio of the amplitudevoltage and current.(c). By using part (a) and (b), as well as the phasor diagram as guides, show that the rmscurrent delivered by the source is1+| @C•R?1I.= Vrms 1rms@L(d). By using part (a) and (b), as well as the phasor diagram as a guide, show that the phaseangle ø between V.and Ims is given byrms1tan ø = R|1Xc X,

“Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

(a). Write the instantaneous currents across the three circuit elements in terms of Vm amp > angular frequency @, inductance L, and capacitance C. (b). Relate for the ratio of the rms voltage and current towards the ratio of the amplitude voltage and current. (c). By using part (a) and (b), as well as the phasor diagram as guides, show that the rms current delivered by the source is 1 I =V. R? rms ms @L

(a). Write the instantaneous currents across the three circuit elements in terms of Vm amp > angular frequency @, inductance L, and capacitance C. (b). Relate for the ratio of the rms voltage and current towards the ratio of the amplitude voltage and current. (c). By using part (a) and (b), as well as the phasor diagram as guides, show that the rms current delivered by the source is 1 I =V. R? rms ms @L

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter6: Power Flows

Section: Chapter Questions

Problem 6.61P

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