For the circuit in the figure, initially the switch S is closed in (b), until the capacitor is charged; then the switch goes to point (a) so that the battery is disconnected and the capacitor, resistor and inductor are connected in series. Once S is connected at point (a), find a) the angular frequency of oscillation for the series circuit b) write the equation for the charge on the capacitor as a function of time with the respective values of Qmax, angular frequency Wd and time T c) make the Q(t) graph showing explicitly the envelope of the exponential decay (Hint: use geogebra or an application of your choice to obtain a graph).
Sinusoids And Phasors
Sinusoids are defined as the mathematical waveforms that are used to describe the nature of periodic oscillations.
Circuit Theory
Electric circuits are a network that comprises of a closed-loop, which helps in providing a return path for the current through a switch. When the switch is activated, the load operates, and the current accepts a path to finish the circuit at a low potential level from the opposing high potential level. Electric circuits theory is a linear analysis that helps in establishing a linear relation of voltage and current for R (resistance), L (inductance), and C (capacitance).
For the circuit in the figure, initially the switch S is closed in (b), until the capacitor is charged; then the switch goes to point (a) so that the battery is disconnected and the capacitor, resistor and inductor are connected in series. Once S is connected at point (a), find
a) the angular frequency of oscillation for the series circuit
b) write the equation for the charge on the capacitor as a function of time with the respective values of Qmax, angular frequency Wd and time T
c) make the Q(t) graph showing explicitly the envelope of the exponential decay (Hint: use geogebra or an application of your choice to obtain a graph).
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