University of Illinois Sp 2016ECE210 / ECE211 - Homework 061. In the following circuit determine the node-voltage phasors V1, V2, and V3and express them in polar form.2. In the circuit shown for Problem 1, determine the loop-current phasors I1, I2, and I3and express them in polarform.3. Use the phasor method to determine v1(t) in the following circuit:+-+-v2(t)2cos(4t)V4ix(t)ix(t)1H116Fv1(t)2Ω4. Use the following network to complete (a) and (b):(a) Calculate the equivalent impedance of the following network for (i) ω = 5 krad/s, (ii) ω = 25 krad/s, and(iii) ω = 125 krad/s.(b) Assuming a cosine voltage input to the network with a fixed amplitude and variable frequency ω, at whichvalue of ω is the amplitude of the capacitor voltage maximized? At the same frequency, what will be theamplitude of the resistor current?+23V23⌦ab3 HW64 Problem 4.14(a) Calculate the equivalent impedance of the following network for (i) ! =5krad/2, (ii) ! = 25krad/s, and (iii ) ! = 125 krad/s.(b) Assuming a cosine voltage input to the network, with a fixed amplitudeandvariable frequen cy !, at which value of ! is the ampl i t ud e of the capacitorvoltage maximiz e d? At the same frequency, what will be the amplitude of theresistor current?2µF50⌦0.8mHSolution:Convert the circuit into f r eq u en cy domain:1j!CRj!L35. Use the following network to answer (a) through (d):+-+-VVsIs1j 11j 3j 1R1R2(a) Determine the phasor V when Is= 0.Page 1 of 2(b) Determine the phasor V when Vs= 0.(c) Determine V when Vs= 4 V and Is= −2 A, and calculate the average power absorbed in the resistors.(d) What is the Thevenin equivalent and the available average power of the network when Vs= 4 V andIs= −2 A?6. Determine the impedance ZLof a load that is matched to the following network at terminals a and b, anddetermine the net power absorbed by the matched load:Page 2 of