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I know we usually consider the time constant for an RC circuit to be τ=RC, because that's the time for the current drop to 1/e of its max value. In this case the author may be considering the time constant to be the time it takes for the power to drop to 1/e of its max value, in which case τ=RC/2.The calcs look good.
I'm quite uncomfortable with that P = I²R, which is the formula for the power dissipated by the resistor. But the battery also delivers power to the capacitor. Better to use P = IV. The V is constant, so all you have to worry about is the I. At what time does I decay to half its initial value?
Well thanks ... it worked !!!I'm quite uncomfortable with that P = I²R, which is the formula for the power dissipated by the resistor. But the battery also delivers power to the capacitor. Better to use P = IV. The V is constant, so all you have to worry about is the I. At what time does I decay to half its initial value?
No i'm pretty sure that τ=RC.i know we usually consider the time constant for an rc circuit to be τ=rc, because that's the time for the current drop to 1/e of its max value. In this case the author may be considering the time constant to be the time it takes for the power to drop to 1/e of its max value, in which case τ=rc/2.
Just a thought.
But 0.5 Q²/C is not power but energy delivered by battery,It is interesting to work it out again using P = i²R + 0.5 Q²/C.