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In an LC circuit as shows in Fig. the sw...

In an `LC` circuit as shows in Fig. the switch is closed at `t = 0`.`Q_(max) = 100 mu C`, `L = 40 mH`, `C = 100 mu F`.
a. Determine the equation for instantaneous change on the capacitor.
b. Determine the equation for instantaneous current in the circuit.

Text Solution

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a. `q = Q_(max) cos omega t`, Here `Q_(max) = 100 mu C`,
`omega = (1)/(sqrt(LC)) =(1)/(sqrt((40 xx 10^(-3))(100 xx 10^(-6)))) = 500 rads^(-1)`
`q = 100 cos (500t) mu C`
b. `i = (-dq)/(dt) = (100) (500) sin (500t) mu A`
or `i = 50000 sin (500t) mu A`
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