When a non-driven RLC circuit discharges you have several possibilities: underdamped, critical & overdamped. The general solution of the differential equation is Q(t) = A*exp(L1*t)+B*exp(L2*t) with L1 and L2 roots of the characteristic polynom being (-R+sqrt(R^2-4*L/C))/(2*L) and (-R-sqrt(R^2-4*L/C))/(2*L)(adsbygoogle = window.adsbygoogle || []).push({});

In the critical case R^2-4*L/C is zero, in the overdamped case it is larger than zero.

Now in class we were told that in the critical case the charge always approaches faster to zero than in any overdamped case. I tried to figure out why but I don't seem to find the answer. I thought it had to do with the fact that in the critical case the characteristic polynom only has one root and in the overdamped it has two but I can't seem to find any mathematical proof of the charge going faster to zero.

If anyone has an idea as to how to prove this, it would be most welcome. :)

Thanks.

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# Homework Help: Uncharging RLC circuit, critical & overdamped case

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