Question 1 A circuit has in series an electromotive force given by E(t) = E, sin(wt) V, a resistor of R, an inductor of L H, and a capacitor of C Farads. a) Show that the steady-state current is 1 where X = Lw- Ca R X =sin out-cos out). wt is the reactance of the circuit and Z=√√x²+R2 is the impedance. b) Using the result of part (a), show that the steady-state current [12] may b y be written as Eo i = Z sin(wt - 6) where is determined by the equations R coso =, sino = KIN z' c) Show that the amplitude of the steady-state current is a maximum when 1 W= VLC For this value of w electrical resonance is said to occur. [3] [3] d) If R = 20, L = C = 10-4, and Eo = 100, find the value of w that gives rise to electrical resonance and determine the amplitude of the steady-state current in this case. [2]