Question

# Figure 1 shows a circuit consisting of two resistors, a capacitor and a voltage source. The switch is left open for t < Os. At t = Os, the switch

is closed. The following questions apply to currents and voltages in this circuit, when the switch goes from being open to being closed. Note that the capacitor looks like an open in the steady state, and the voltage across the capacitor cannot change instantaneously. (a) When the switch is open for t < Os, find the currents in the resistors, R1 and R2. (6) (b) When the switch is open for t < Os, what is the voltage across the capacitor. (6) (c) When the switch is open for t < Os, find the charge and energy stored in the capacitor. (6) (d) Immediately after the switch is closed at t = Os, find the voltage across the capacitor. (4) (e) Immediately after the switch is closed at t =Os, find the current in resistor R2. (6) (f) Immediately after the switch is closed at t = Os, find the voltage and current in resistor R1. (g) Immediately after the switch is closed at t = Os, find the current in the capacitor. (7) (h) Long after the switch is closed, what are the currents in the resistors, R1 and R2. (6) (i) Long after the switch is closed, what is the energy stored in the capacitor. (5) (j) After the switch is closed, find the Norton equivalent current (Is) and resistance (R) acrossthe terminals of the capacitor as shown in figure 2. Use source transformation to find theNorton circuit. (8) (k) se the Norton model in figure 2 with the step response of a RC circuit to write the voltage across the capacitor in the form v_{c}(t)=I_{s} R+\left(V_{0}-I_{s} R\right) e^{-t / \tau} Find Is, R, Vo and t. (10) (1) Using the relationship between capacitor voltage and current, find an expression for the current through the capacitor in terms of Is, R, Voand z. (8) (m)Find the peak current through the capacitor. At what time does the peak current occur.Note you don't have to find the derivative in this case. (7) (n) Find the time when the current is down to 50% of the peak value in part (m) (8) (0) If the value of resistor, R2, is changed such that the voltage across the capacitor when t→00 is one half the voltage across the capacitor for t<0, find the new value of R2. (7)

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