The time-varying current in an LC circuit where C = 11.9 µF is given by i(t) = (

Question

The time-varying current in an LC circuit where C = 11.9 µF is given by i(t) = (1.25 A) sin (1310t), where t is in seconds.

a) At what time after t = 0 does the current reach its maximum value?
b) What is the total energy of the circuit?
c) What is the inductance, L?

Explanation / Answer

a) for current to be max 1310t = pi/2 => t = 1.2 ms c) w = 1310 = 1/sqrt(LC) => L = 0.049 H b) v(t) = Ldi/dt = L (1.25A) *1310 * cos (1310t) total energy = 1/2 cV^2 + 1/2 L I^2 but at t=0 i(0) = 0 => total energy at t=0 is E(0) = 1/2 CV^2 = 0.447 mJ since there is no resistive element E(t) is constant so total energy = 0.447 mJ

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