Why is the current through I2 constant?

[kd2amc]

Homework Statement

I was going through this PDF to review for my AP Physics C E&M exam: https://apcentral.collegeboard.org/...course=ap-physics-c-electricity-and-magnetism

I was also watching this video (which discusses the solutions):

I am stuck on part 2(b) (page 7 of the PDF, 17:18 minute mark of the video)

Homework Equations

The solution uses V=IR. I didn't use any equations in my attempt at solving the problem.

The Attempt at a Solution

I originally thought that I2 would increase, because when the switch is first closed, the capacitor acts like a wire and allows current to flow freely, so the current will be split between both the R1 and R2 parallel branches. Then, after a long time, the capacitor acts like an open switch, so no current will flow through R1 and it will all flow through R2 - therefore, the current in R2 would increase. After watching this video, I understand the instructor's reasoning as to why I2 remains constant (namely, that I = V/R and V and R are both constant, so I is constant), but I'm not sure what was wrong with my original thinking.

Thank you so much for any assistance! I really appreciate your time and help.

 

[lewando]

At the moment when the switch is closed, what is the voltage across R₂?

 

[kd2amc]

At the moment when the switch is closed, what is the voltage across R₂?

I believe it is equal to V₀.

 

[lewando]

Does it ever change thereafter?

 

[kd2amc]

I see what you are saying - the voltage remains constant and the resistance remains constant, therefore the current remains constant. Thank you!