Problem 3: For the circuit shown here, the current and voltage are as follows: vs(t) 17cos(wt-45°) V is(t) 50sin(wt-120°) A Answer the following questions: a) For w=377 rad/s, determine the impedance, Z. Z=(-0.328 + j0.088) b) Although the individual circuit elements contributing to the impedance Z are not known, is it possible that they are all resistors? Explain the reasoning supporting your answer. c) If w=100 rad/s, and the voltage and current remain as shown above, has there been a change to the values of one or more of the individual circuit elements contributing to the impedance? Explain the reasoning supporting your answer. Problem 4: The circuit shown here contains an AC voltage source. Determine the current phasor, IR, using the following circuit element values given in terms of phasors and impedances: Vs=20V R₁ =9 R₂-170 L₁ =140 C₁ = -j5n L₁ R₂ Problem 5: Since capacitors and inductors cause opposite phase shifts (+90°) between their voltage (1) and current in an AC circuit, =1.52e77.3° a R₁ R₂ they can be used together to keep current and voltage in phase for maximum power delivery. In the circuit shown here, a capacitor has been placed in parallel with an inductor (e.g., motor) to keep the voltage and current in phase. For w = 10* rad/s, determine the value of C needed to keep v(t) and i(t) in phase for the following circuit element values: R₁ = 50 R₂ =250 L= 2.5 mH C=4F Hint: For i(t) to be in phase with s(t), the equivalent input impedance Z seen by the source must be purely real.