I'm fairly certain that this isn't a problem, but like a phone charger it will still pull electricity even though you aren't charging anything if you leave it plugged into the wall. Though minimal it still pulls power. Does the same apply to ethernet cables? If I have a router and I have a cable going to nothing. Say I have a laptop that I plug in when I'm on the couch, but I unplug it when I'm done and put my laptop away. Will that ether still pull bandwidth from my router even though it is not connected to anything? I would assume not because there is no data being sent through that cord, but like a phone charger..
As mentioned by others there is no way that an unplugged Ethernet cable can consume bandwidth. There simply is nothing to send data to in order to waste the bandwidth.
The "wall-wart" power adaptors for mobile phones are power-converters. In order to do their job they have some active components such as transformers and regulators which convert the high mains voltage down to the voltage expected by your mobile phone. Those electronics waste a percentage of power (typically around 10% of whatever power they draw is wasted by this conversion) in order to present the correct voltage to your device. Even when nothing is connected they still have to present the correct voltage at the output, unless there is a switch to turn it off, and so this is where they waste power.
Ethernet bandwidth is different, Ethernet is not a power supply device, it is used for signalling devices and over the years the electronics behind the devices have gotten more and more intelligent.
Typically any modern network router is able to "sense" whether or not a device is connected to any given port and so disable that port if needs be. This "sense" will waste an absolutely tiny amount of power but because the device knows that there is nothing on that port it will not bother to attempt to send data to it, so no bandwidth wasted there...
Even if it did try to send a data packet asking "Is anybody there?" then the amount of bandwidth it might use compared the full Ethernet bandwidth is so miniscule it would be be completely undetectable and even then I would expect this to be handled by the physical port controller rather than the rest of the hardware and so it wouldn't be able to waste bandwidth that way either.
Bandwidth is not the same as electricity. Electricity is like water: It goes wherever it can, filling each available space according to the rules of physics, unless acted upon by some force.
Laws of physics to not apply to bandwidth or network communication. An unconnected network cord should not take up and network resources. It may get a little bit of electricity as the router tests to see if there's something at the other end, but a little electricity does not equal network bandwidth.
Ethernet bandwidth is used to transfer coded information. When you leave a telephone off hook while there is still a connection, any sound is going to be transmitted and will use bandwidth. It's a little different with newer telephone technology, because the phone acts like a gate keeper, blanking out sound below a set threshold level so that it doesn't consume bandwidth during quiet times. Ethernet is a little more sophisticated, because the gate keeping is done by switches or routers that look for data that is coded a particular way before it can be forwarded.
Any electrical signals (noise, for example) on your dangling Ethernet cable are unlikely to resemble a properly coded signal. Therefore, they will not satisfy the gate keeping requirements of the switch or router that the cable is connected to, and will not consume any bandwidth.
It wouldn't matter anyway, since your router has dedicated bandwidth to each Ethernet port. Even if it used all the bandwidth, that would have no effect on anything. If you mean bandwidth over your Internet connection, machines only send responses to specific requests. A stray length of wire can't issue any requests. (What other machine would it talk to? How would it find it?)
Also, your analogy really doesn't work. The charger pulls electricity because it is connected to the outlet. There's nothing connected to the charger, but no electricity passes over the charger wire. The unconnected charger wire pulls no additional electricity over what the charger itself pulls.
Just like there would be no difference between having just the charger plugged in with no wire and having the charger plugged in with a long wire not connected to anything, there would be no difference between just having your router plugged in with no wire and having the wire plugged in not connected to anything. In both cases, the wire has no effect, but the connected device still does what it does even with nothing else connected to it.
In most cases the router can detect whether something is connected to the other end and will only attempt to talk to the other end if there's a connection. And even if the router thinks it detects something it will at most do an occasional ping of the other end (though I believe the standard protocol calls for the other end to initiate conversation). So at most the cable is consuming an occasional few cycles from the router's processor -- nothing that would affect capacity. Absolutely nothing due to this "goes out" over the "outside world" connection, which is your major capacity bottleneck.
On the other hand, having the cable attached DOES cause a miniscule additional power draw, due to capacitive and leakage losses, but probably not enough to measure, even with lab instruments.