Answer to Question #236181 in Classical Mechanics for alwande hadebe

Question

When there is a flow of charge q in an electric circuit containing a resistor R, capacitor C and inductor

L, there is a direct analogy with the moving parts of a mechanical oscillator comprising a mass m and a spring

with spring constant k. If a series LRC circuit is connected across a voltage source given by V = Vo cos ωt, the

flow of charge through the circuit is given by the following second order differential equation:

Lq¨+ Rq˙ +

1

C

q = V0 cos ωt.

(a) Determine the correspondence between the parameters of a driven mechanical oscillator (as discussed in

the notes) and the above driven electrical oscillator.

(b) Calculate the quality factor Q of the electrical circuit in terms of the coefficients of the above differential

equation.

(c) Show that, in the case of small or light damping, Q can be written as Q = R0/R, where R0 =

p

L/C is

the characteristic impedance of the circuit.

Answer 1

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