problem with Get-ADuser

Hi friends

i have lost my patiense & i will cry.

it's about 1 hour that i am struggling with a simple issu.

in my domain i have 3 users called u1, u2, u3    both names & samAccount names are same for each user.

when i run 

Get-Aduser -filter {name -eq "u1"}   ----> it works

but followings doesn't work & show no output:

$i = 1

Get-Aduser -filter {name -eq "u$i"}   ----> no result (nothing is shown in output)

help please