- #1

mymodded

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- TL;DR Summary
- in RLC circuit with capacitor fully charged initially, ##q(t) = q_{max} e^{-Rt/2L} \cos(\omega t)## , if we want ##i(0) = \frac{d q}{dt}|_{t=0}## we don't get 0 as expected, whats wrong?

suppose that we have an RLC circuit where initially, the capacitor is fully charged, the charge in the capacitor is given by ##q(t) = q_{max} e^{-Rt/2L} \cos(\omega t)##, if we want to find the current, we would differentiate the charge, so $$\Large i(t) = \frac{d q}{dt} = \frac{d}{dt} (q_{max} e^{-Rt/2L} \cos(\omega t)) = q_{max} (-\frac{R}{2L}e^{-Rt/2L} \cos(\omega t) -\omega e^{-Rt/2L}\sin(\omega t))$$

we know that the current at t = 0 has to be equal to 0A (since the capacitor is fully charged), but if we plug in t = 0 in i(t) we don't get 0A, so what's wrong?

we know that the current at t = 0 has to be equal to 0A (since the capacitor is fully charged), but if we plug in t = 0 in i(t) we don't get 0A, so what's wrong?