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## Homework Statement

There is a circuit with a battery of voltage V and resistor R, then splits into two branches one with a capacitor C, and one with a resistor 2R.

The answers for the questions can only depend on R, C, V, and t.

When a switch only allows current to flow through the capacitor branch, the expression for charge is:

##Q = C V (1-e^{-t/(RC)})##

a) When the switch is closed, find an expression for the charge on the capacitor after a very long time (t >> RC)

b) When the switch is closed, find an expression for the current through the battery after a very long time (t >> RC)

## Homework Equations

##Q = C V (1-e^{-t/(RC)})##

Current through resistor R:

##I = (V / R) e^{-t/(RC)}##

Current through resistor 2R:

##I = (-V / 2R) e^{-t/(2RC)}##

## The Attempt at a Solution

a) I tried taking the limit of the charge as t goes to infinity and got my answer to be CV, but I only received 1/4 possible points for the problem so I either didn't do it right or didn't show all the work.

b) I tried taking the limit of the current and t goes to infinity and got my answer to be 0, but that is also wrong.