The characteristic equation of a system is found to be: s“ + 5s² + 3s + 1 This system is: a. unstable b. stable Oc. marginally stable Od provided information is not enough

From the circuit shown below calculate the following + Vc - C=0.05pf 10V R1=100k R2=100k a) Find the mathematical expression for the voltage across the capacitor from the previous figure, if the switch is set to position 1 at t=0s. Calculate the voltage vc in t=10ms. Repeat the previous for ic and VR,- b) Find the mathematical expression for the voltages vc and VR, and the current iç if the switch is set to position 2 at t=30ms (Assume that the leakage resistance across capacitor =c0ohms) c) Find the mathematical expression for the voltages ve and (VR, + VR2) and for the current ic, if the switch is set to position 3 at t=48 ms. Find the voltages vc and VR + VR2 and the current iC at t = 100ms. d) Plot the waveforms obtained in the previous on the same time axis for each voltage and for current.

For the circuit shown in Figure 3: A +1 V1 9V S1 B R1 1kQ2 C1 470μF The circuit in Figure 3 shows the circuit set up to charge and discharge a capacitor. a) Calculate the time constant (T) for the circuit. b) Draw the detailed current waveform through the circuit and voltage waveform across capacitor for the Capacitor charge cycle when the switch is at position A. (Consider the initial capacitor voltage to be OV). c) Draw the detailed current waveform through the circuit and voltage waveform across capacitor for the Capacitor discharge cycle when the switch position is changed to position B. (Consider the capacitor to be fully charged just before the switch position is changed). The waveforms should be labelled, showing the capacitor voltage, currents and time constant. The figures should show as much details as possible, including the time constant and voltage levels. Also write a brief description, explaining the behaviour of the capacitor under the two mentioned cycles.

the capacitor