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{"ops":[{"insert":"When there is a flow of charge q in an electric circuit containing a resistor R, capacitor C and inductor\nL, there is a direct analogy with the moving parts of a mechanical oscillator comprising a mass m and a spring\nwith spring constant k. If a series LRC circuit is connected across a voltage source given by V = Vo cos \u03c9t, the\nflow of charge through the circuit is given by the following second order differential equation:\nLq\u00a8+ Rq\u02d9 +\n1\nC\nq = V0 cos \u03c9t.\n(a) Determine the correspondence between the parameters of a driven mechanical oscillator (as discussed in\nthe notes) and the above driven electrical oscillator.\n(b) Calculate the quality factor Q of the electrical circuit in terms of the coefficients of the above differential\nequation.\n(c) Show that, in the case of small or light damping, Q can be written as Q = R0\/R, where R0 =\np\nL\/C is\nthe characteristic impedance of the circuit.\n"}]}
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