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a) A resistor and an inductor are connected in series, as shown in the Fig. 1below. You are reminded that the impedance of an ideal inductor is given byZL iw L. Given that the inductor has a value of 2 mH, and the resistor is1002, calculate the total complex impedance of both components connectedin series at a frequency of f = 5 kHz. [8 marks]

A long solenoid is made by winding N coils of wire around a hollow cyclindricalcore of cross-sectional area 1 × 10-4 m². The length of the solenoid is 0.1 m.Calculate the number of turns, N, required to construct a inductor of 2 mH.You are reminded that the inductance of a long-solenoid is given by L=\frac{\mu_{o} A N^{2}}{l} where A is the area of the solenoid, I the length and po is the permeability offree-space, which can be taken as 1.257 × 10-6 Hm¯¹. [6 marks] The capacitance of an ideal parallel plate capacitor is given by C=\frac{\epsilon_{0} \epsilon_{r} A}{d} where to is the permittivity of free space, which can be taken as 8.854 × 10−¹² F m¯¹,0.01 m² is the area of the plates and,is the relative permittivity, AEr,d=1 x 10-4 m is the plate separation. (i) If the region between the capacitor plates is filled with a material that has a dielectric constant of 3, what will the capcitance be? [3 marks] (ii) If the capacitor is charged up to a potential of 10 V, how much energy will be stored in the capacitor? [3 marks]

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