There is circuit with one resistor, one capacitor, one switch and a dc voltage source

Question

resistor = 200Ω
dc voltage = 10v
Capacitor = 10 uf = 0.00001f

1. what is the RC time constant of the circuit?
answer: (200Ω)(0.00001f)=0.002s

2. What is the time from the instant that the switch closes until the capacitor fully charges? Assume that the capacitor is fully discharged prior to the switch closing?
answer: t=5*(rc)
t= 5*(0.002) = 0.01s = 1ms

3. What is the current in the circuit the instant after the switch closes? Assume that the capacitor is fully discharged prior to the switch closing.
answer: i=v/r = 10v/200Ω = 0.05A

are my answers correct?

Answer 1

If the circuit is a series RC, all are correct.

Answer 2

it is in a series rc circuit