I condensed it a bit. This is closer to how I would do it:

#!/usr/bin/perl -sl

BEGIN { $^W = 1; }
sub BEGIN {
    if ($^W == 1) {
        print "Let's get started...\n";
    }
    else {
        die $@;
    }    
}

use strict;
use warnings;
use English qw(-no_match_vars);

local $OUTPUT_AUTOFLUSH = 1;
local $OUTPUT_RECORD_SEPARATOR = *\ ;

print "I will calculate whatever \n", 
      "you specify according to\n", 
      "Ohm's law. What shall I\n", 
      "calculate? Type either\n ",
      "voltage, current, or \n", 
      "resistance.\n";
      
my $i = 0;
while ($i == 0) {
    my $calculation = <STDIN>;
    if ($calculation =~ /voltage/) {
        print "Type the current of the circuit.\n", 
               "Add mA at the end of your answer\n", 
               "if your answer is in milliAmps.\n";
        chomp(my $current = <STDIN>);
        print "Now type the resistance of the circuit.\n";
        chomp(my $resistance = <STDIN>);
        if ($current =~ /mA/) {
            $current =~ s/mA//;
            $current =~ s/^\s+//;
            $current =~ s/ //;
            $current /= 1000;
        }
        else {
            ();
        }
        my $voltage = $current * $resistance;
        print "Ohm's law is V = IR, so the voltage of\n";
        print "the circuit is $voltage volts.\n";
        ++$i;
    }
    elsif ($calculation =~ /current/) {
        print "Type the resistance of the circuit.\n";
        chomp(my $resistance = <STDIN>);
        print "Now type the voltage of the circuit.\n";
        my $voltage = <STDIN>;
        my $current = $voltage / $resistance;
        my $otherCurrent = $current / 1000;
        print "Ohm's law is V = IR, so the current of\n",
              "the circuit is $current amps\n", 
              "or $otherCurrent milliAmps.\n";
        ++$i;
    }
    elsif ($calculation =~ /resistance/) {
        print "Type the current of the circuit.\n",
              "Add mA at the end of your answer\n",
              "if your answer is in milliAmps.\n";
        chomp(my $current = <STDIN>);
        print "Now type the voltage of the circuit\n.";
        my $voltage = <STDIN>;
        if ($current =~ /mA/) {
            $current =~ s/mA//;
            $current =~ s/^\s+//;
            $current =~ s/ //;
            $current /= 1000;
        }
        else {
            ();
        }
        my $resistance = $voltage / $current;
        print "Ohm's law is V = IR, so the resistance of\n", 
              "the circuit is $resistance ohms.\n";
        ++$i;
    }
    else {
        print "That is not a valid answer.\n" 
        "Retype your answer.\n";
    }
}
[download]

Update: made a few additions.