#### Is it true that if you double the current through a wire then you double the voltage loss and if you halve the current then you halve the voltage loss?

Yes. When you try to push current through a wire, the voltage drop across that wire (i.e. the energy lost by each charge passing through that wire) is proportional to the number of charges flowing through that wire each second (i.e. the current through the wire). If you double the number of charges flowing through the wire each second, then each charge will lose twice as much energy (the voltage drop across the wire will double). If you halve the number of charges flowing through the wire each second, then each charge will lose half as much energy (the voltage drop across the wire will halve).