Well, assume that the CNT material is just as conductive as pure copper. <br /><br />First problem is that you need two conductors minium to carry power. I'm assuming that it will be DC and not 3 phase AC.<br /><br />So, assuming that the conductors are as good as copper and the intervening material is a really good insulator.<br /><br />What is the cross sectional area of the elevator cable. Remember that you have to divide by two because of two conductors and then subtract out the insulator section.<br /><br />The insulator section will have to be pretty good to support any voltage difference. Arcing would be a major problem since that would probably destroy the elevator cable.<br /><br />There is also the problem of coupling the car to the cable in a way that doesn't scratch or damage the cable in any fashion. That isn't necessarilly a trival problem.<br /><br />Look at the electrical coupling for a electric rail car, and you see sparks as it goes down the track . On a space elevator those sparks would be very damaging to the cable.<br /><br />Any case, assuming you solve all of those problems. Look at the cross sectional area of the conductor. Remember that you have to transmit the current tens of thousands of miles. To transmit any significant power is going to require significant voltage or your ohmic losses are going to eat up all of the power.<br /><br />If your transmitting power on the ground for hundreds of miles. The typical voltage is 115KV Three phase AC.<br /><br />At 115KV you need monster large insulators. The climber car is going to have to deal with that huge voltage. Very few motors are built at that voltage, because the insulation requirements are huge. <br /><br />Even at that voltage, there are significant power loses over a couple of hundred miles. At 10,000 plus miles, the power losses would be staggering.