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2. The LC circuit’s charge could be described by this second-order differential equation L d2qdt2+C q=0 where q is the...

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Physics

2. The LC circuit’s charge could be described by thissecond-order differential equation

Ld2qdt2+Cq=0

where q is the time-dependent charge in the circuit, L isinductance, and C is the capacitance.

The solution to that equation isqt=q0cos(ωt+ϕ) where q0 is the maximum charge in the circuit, wis the angular frequency of the circuit, which equals1L C , and f is the phase angle of thecircuit.

a. What does q(t) represent? Yes, I know it means “the charge”but of what? After all, the circuit has the same number ofelectrons and protons regardless of whether there is currentflowing or not, so what does that quantity mean?

b. In order for the initial charge to be zero; that is, q(0) =0, what does the phase angle f need to be?

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