Question

Chapter 31, Problem 024 GO A single-loop circuit consists of a 7.2 2 resistor, 12.1 H inductor, and a 3.3 uF capacitor. Initially the capacitor has a charge of 6.0 C and the current is zero. Calculate the charge on the capacitor N complete cycles later for (a) N = 5, (b) N =10, and (c) N = 100. (a) Number Units (b) Number Units (c) Number Units

Answer 1

chare after 'N' cycles

t = N * T

where T = 2$\pi$ / w

so,

q = Qe^{-Rt / 2L} cos ( wt + $\phi$ )

from this we get

q = q_o e^{( - N$\pi$R sqrt ( C/L))}

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(a)

for N = 5

q = 6 e^{( - 5$\pi$* 7.2 sqrt ( 3.3e-6/12.1))}

q = 5.655 uC

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(b)

for N = 10

q = 5.332 uC

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(c)

for N = 100

q = 1.8413 uC