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# Question 1 (60 marks) (a) The combination of resistors capacitors C1, C2, C3 and C4 in Fig. 1(a) is equivalent to a single capacitor Ceq. Calculate the value of Ceq when C1 = (1000 + a) nF, C2 = (2000+ B) nF, C3 = (3000 + y) nF and C4 = (4000 + ō) nF. C1 Ceq C2 C4 C3 Figure 1(a) Ceq 15%/n(b) Referring to Fig. 1(b), calculate the dc steady state voltage VL across the load resistor RL. Rs = (50 + 5) Q, C1 = (2000 + ε) nF, L2 = (300 + a) µH, C3 = (4000+ 0) nF, and RL = (50 + A) Q. Vs= 3 V. Rs Vs VL (in dc steady state) SPICE circuit schematic C1 L2 Figure 1(b) C3 RL + VL 15% 5%/n(c) Calculate the magnitudes and phases of the phasor representations of the following quantities: (1) (ii) (III) (iv) (i) (ii) where f = (1000 + 3) kHz, Is = (100 + a) μA, Vs (2500 + 5) mV, R = (1800 + ε) Q2, L= (2200 +λ) µH, C = (470+ n) pF, (iv) i₁ (t) = 1, cos(wt + 0.5) v₂ (t) = V.sin(wt - 1.2) 2 Z3 (w) = R + jwL R Magnitude (with units) Z4 (w) = 1 + jwCR Phase (degrees) Phase (radians) 30%/n(d) At time t = 0, the capacitor C in Fig. 1(d) is charged to Vc = +1V and the switch S is open. The switch is closed at time t = 100 µs, connecting the voltage source Vs to the RC network. Calculate the voltage on the capacitor at time t = 200 µs. ⒸUCD 2023/2024 Page 5 of 8 Vs = (3000 + a) mV, R = (2200 + B) Q, and C = (100 + y) nF. S Vc(200µs) Vs R www + C = Vc Figure 1 (d) 20%  Fig: 1  Fig: 2  Fig: 3  Fig: 4