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Consider the circuit in which a battery

with internal resistance r can be connected via a switch to a resistor

and capacitor in parallel.

Suppose that the capacitor is initially uncharged and then at time

t = 0 the switch is closed. After the switch is closed a current I_b(t)

flows through the battery, a current I_R(t) flows through the resistor

with resistance R, and the charge on the upper plate of the capacitor increases at a rate

dq/dt .

-What is dq/dt for times t ≥ 0 ?

-What is dq/dt at t = 0 ?

-What is I_R (t = 0)?

-What is the voltage VC across the capacitor at t = 0 ?

-What is dq/dt at very long times ( t → ∞ )?

-What is the voltage VC across the capacitor at very long times?

-Is VC at very long times less than, equal to, or greater than ε ?

-What is I_R (t → ∞) ?

So I'm been wrestling with this question fr a while. I know through loop rule that the current across the resistor is equal to Q/CR (from a loop of just the capacitor and resistor). I solved the differential for charge and found q(t)= EC/2 (1-e^(-2t/CR)). And I know how the whole system would act if the capacitor and resistor were in series but I'm really stuck. Any help would gladly be appreciated!