In an LC circuit the total charge stored is Q0. For t >= 0, which statement(s) about the charge Q on the capacitor is/are correct?

Q = Q0*cos(pi/2 + t/sqrt(L*C))
Q = Q0*cos(pi/2 - t/sqrt(L*C))
Q = -L*C*(d²Q/dt²)
Q = -(1/sqrt(L*C))*(d²Q/dt²)

Correct answer: Q = -L*C*(d²Q/dt²)

Solution

The LC circuit satisfies L*(d²Q/dt²) + Q/C = 0, i.e., d²Q/dt² = -Q/(LC). Rearranging: Q = -L*C*(d²Q/dt²), which is option (C). The cosine option cos(pi/2 - t/sqrt(LC)) = sin(t/sqrt(LC)) starts at Q=0, not Q0, so it is not the charge here; the dimensionally inconsistent last option is wrong.

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