Answer to Question #210713 in Classical Mechanics for Rae

Question

a) The resistor of an RC circuit has a resistance of 10 MΩ, the time constant is 1 s. What is the capacity of the capacitor? b) To what percent of the original value does the voltage of the capacitor decrease in 2 s?

Answer 1

a)

$C=\frac{T}{2\pi R}=\frac{1}{2\cdot 3.14\cdot 10\cdot 10^6}=15.9~nF,$

b)

$R=\frac{T'}{2\pi}(\frac{1}{C'}-\frac 1C),\implies$

$C'=(\frac 1C+\frac{2\pi R}{T'} )^{-1}=6.36~nF,$

$p=1-\frac{C'}{C}=0.6=60\%.$