A coil with internal resistance can be modeled as a resistor and an ideal induct

Question

A coil with internal resistance can be modeled as a resistor and an ideal inductor in series. Assume that the coil has an internal resistance of 1.80 and an inductance of 420 mH. A 2.60 µF capacitor is charged to 22.0 V and is then connected across the coil.

(a) What is the initial voltage across the coil?
V

(b) How much energy is dissipated in the circuit before the oscillations die out?
mJ

(c) What is the frequency of oscillation of the circuit? (Assume the internal resistance is sufficiently small that it has no impact on the frequency of the circuit.)
Hz

(d) What is the quality factor of the circuit?

Explanation / Answer

(a)

initial voltage 22 V

(b)

U = 1/2 * CV^2 = 1/2 * 2.6 * 10^-6 ( 22)^2 = 0.629 mJ

(c)

fo = 1/2pi sqrt LC = 1/2pi sqr (0.420)(2.6 * 10^-6) = 152.38 Hz

(d)

Q = woL/R = 1/R sqrtL/C

= 1/1.80 sqrt (0.420/2.6 * 10^-6)

=401.91

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