- #1
iScience
- 466
- 5
I'm having a brain fart so this is just another silly question but...
when deriving the I-V relation for the capacitor:
$$C=\frac{dq}{dV}$$
$$\frac{d}{dt}C=\frac{d}{dt} (\frac{dq}{dV})=\frac{d}{dt}C=\frac{di}{dV}$$
from here, normally we're supposed to do the following
$$\int\frac{dC}{dt}dV=i$$
$$C\frac{d}{dt}V=i$$
$$C\frac{dV}{dt}=i$$
but even before integrating, where i have quantity: $$\frac{dC}{dt}$$ isn't this just zero?
in which case, if we integrate both sides with V i just get 0 on the LHS so i know it's not valid..
but why is it not valid?
when deriving the I-V relation for the capacitor:
$$C=\frac{dq}{dV}$$
$$\frac{d}{dt}C=\frac{d}{dt} (\frac{dq}{dV})=\frac{d}{dt}C=\frac{di}{dV}$$
from here, normally we're supposed to do the following
$$\int\frac{dC}{dt}dV=i$$
$$C\frac{d}{dt}V=i$$
$$C\frac{dV}{dt}=i$$
but even before integrating, where i have quantity: $$\frac{dC}{dt}$$ isn't this just zero?
in which case, if we integrate both sides with V i just get 0 on the LHS so i know it's not valid..
but why is it not valid?
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