Question
Asked Aug 4, 2019
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A single-loop circuit consists of a 7.0 Ω resistor, 12.2 H inductor, and a 3.1 μF capacitor. Initially the capacitor has a charge of 6.1 μC 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.

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Expert Answer

Step 1

Given,

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Resistance, R = 7.0 capacitance, C 3.1 x10F inductance, L 12.2H initial charge on capacitor, q(t =0) = 6.1x10 C

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Step 2

In this LCR oscillation, Charge flow in the circuit is a function of time.

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'-tR qqe2cos('t + ¢ At, t 0 qae° cos (0+ qa, cos() charge on capacitor at / = 0, q = 6.1x10 C hence .cos () = 6.1x10-'C

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Step 3

Angular frequency of LC...

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1 R |LC (2L) (7.0) (12.2H)(3.1 x10F) 2(12.2H) 1 162.6 rad/s

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