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3. (a) An AC current i (f) is represented mathematically in the following form : i(t) = 40 sin(377t- (1/6)] mA Determine the following quantities for i(t): (1) the peak current; (ü) the effective (or RMS) current; (ii) the frequency in Hz; (iv) the phase in degree (state the phase is leading or lagging) 6) A capacitance has a reactance (Xc) of 500 2. It is supplied by a sinusoidal source with an angular velocity (@) of 377 rad/s. (1) Find the value of the capacitance; (ü) Draw the phasor diagram of the capacitance voltage Vc and current Ic. (Remark: Use Ic as reference) () A 220 V 50 Hz a.c. circuit is connected with the loads as shown in Figure 3(C). Given that R1 = 502, R2 = 40 2, X_ = 202, and Xc = 50 2. (1 mark) (2 marks) (2 marks) (2 marks) (2 marks) (2 marks) 220 V, 50 Hz I XL R W- R2 Xc IZ w Figure 3(C) (1) Determine the total impedance of the circuit in polar form. (2 marks) ü) Determine the supply current of the circuit (I) in polar form. (2 marks) (111) Calculate the value Ii in polar form. (2 marks) (d) (1) Briefly explain the reason(s) for using phasor method in the calculations (6 marks) of electrical quantities in AC circuits. (i) State one of the limitation in using the phasor method for calculating (2 marks) AC quantities in electric circuits.