(Solved): (a) (i) What is the resistance, reactance and complex impedance of a resistor ...

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(a) (i) What is the resistance, reactance and complex impedance of a resistor (of resistance \( R \) ), capacitor (of capacitance \( C \) ) and inductor (of inductance \( L \) ) in an \( A C \) circuit operated at an angular frequency \( \omega \) ? Write the complex impedance in both Cartesian and polar form. (3 marks) (b) (i) Consider the series LCR circuit below with \( V_{s}=100 \cos (\omega t) \) volts, \( \omega L=1000 \Omega, 1 / \omega C=1000 \Omega \) and \( R=20 \Omega \). What is the total impedance of this circuit? Comment on the nature of this impedance. (2 marks) (ii) Find the voltage dropped across the resistor, capacitor and inductor (both phase with respect to the source voltage phase and amplitude). (4 marks) (iii) What is the power drawn by this circuit? (1 mark)