Passing bash variable to jq

I have written a script to retrieve certain value from file.json. It works if I provide the value to jq select, but the variable doesn't seem to work (or I don't know how to use it).

#!/bin/sh

#this works ***
projectID=$(cat file.json | jq -r '.resource[] | select(.username=="myemail@hotmail.com") | .id')
echo "$projectID"

EMAILID=myemail@hotmail.com

#this does not work *** no value is printed
projectID=$(cat file.json | jq -r '.resource[] | select(.username=="$EMAILID") | .id')
echo "$projectID"

Consider also passing in the shell variable (EMAILID) as a jq variable (here also EMAILID, for the sake of illustration):

   projectID=$(jq -r --arg EMAILID "$EMAILID" '
        .resource[]
        | select(.username==$EMAILID) 
        | .id' file.json)

Postscript

For the record, another possibility would be to use jq's env function for accessing environment variables. For example, consider this sequence of bash commands:

EMAILID=foo@bar.com  # not exported
EMAILID="$EMAILID" jq -n 'env.EMAILID'

The output is a JSON string:

"foo@bar.com"

shell arrays

Unfortunately, shell arrays are a different kettle of fish. Here are two SO resources regarding the ingestion of such arrays:

JQ - create JSON array using bash array with space

Convert bash array to json array and insert to file using jq