I have a question about the solution for the problem 34 inchapter 18 of the Book

Question

I have a question about the solution for the problem 34 inchapter 18 of the Book College Physics 2. Serway- Vuile.(8th) The question is: A series compacitor of a 12-k and anunknown capacitor is connected to a 12-V battery. One second afterthe circut is completed, the voltage across the capacitior is 10V.Determine the capacitance of the capacitor. In the solution on here, I do not unerdtand how in the middleos the solution it went from 0.1666 to 6.002 and it looks likenothing was done to the equation.? Thanks alot for your help. I have a question about the solution for the problem 34 inchapter 18 of the Book College Physics 2. Serway- Vuile.(8th) The question is: A series compacitor of a 12-k and anunknown capacitor is connected to a 12-V battery. One second afterthe circut is completed, the voltage across the capacitior is 10V.Determine the capacitance of the capacitor. In the solution on here, I do not unerdtand how in the middleos the solution it went from 0.1666 to 6.002 and it looks likenothing was done to the equation.? Thanks alot for your help.

Explanation / Answer

v = v0[1-e^(-t/RC)] v/v0 = 10/12 = 1–e^(–t/RC) v/v0 = 0.8333 = 1–e^(–t/12000C) .8333 = 1-e^(–1/12000C) C = 4.65e-5 F = 46.5F

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