(Solved): Consider the series and parallel RX circuits below. Derive expressions for the parallel circuit va ...

Consider the series and parallel RX circuits below. Derive expressions for the parallel circuit values of Rand X required to ensure the two circuits' impedances match (Z = Ž) at all frequencies and show that they are: R = R (1+x²) and X = X(1 + [Hint 1: Calculate the total impedance for each circuit and compare the real and imaginary parts.] [Hint 2: Recall that Zx =jX for a generic reactive impedance.] [Hint 3: There are many approaches to solving this problem. Some are really quite straightforward. Some can become surprisingly complicated quite quickly. Consider carefully what you are trying to solve for and how best to target that most directly. However, if you find yourself mired in a swamp of complicated polynomials of resistances and reactances, you may find the following very useful. Specifically, note that if Z Ž, then it must also be true that |Z|² = |Z|². If you are finding it hard to eliminate a variable individually, it may be easier to eliminate it as part of eliminating a whole expression.] Series Parallel www www R X Upload your working to the text box below. [Partial marks will be awarded for this question.]