There is a possibility, when a nuclear bomb explodes it sends out an EMP blast which is an electromagnetic pulse, this EMP will make all electrical things, even batteries stop working because it seizes the electrons inside the wires, any wires with current flowing through or electron moving, there is a way to overcome this, simply switch it off before the blast occurs and this will simply protect the electrons in the wires because they are not active and the EMP will have no effect, also doesn't a nuclear blast kill people, in nuclear testing with the military, humans who where close by any blast immediately died, this was unexplained untill the EMP was discovered, the EMP basically jolts your hearth and seizes all your neurons, in order to live you'll have to change the cables in this case your neurons which would be impossible. In the movie "Deja Vu" they simply restart his hearth with an electrocardiogram, that would never work in real life.
New electrical components usually within a whole system can detect an EMP and automatically shuts off current flow to protect its electrons, this is advance electronics, hence new fighter aircraft are not affected by EMP blasts.
But a worldwide EMP would be impossible to make unless you set off nuclear bombs all over the cities killing mankind, plus i still dont know how humans can survive an EMP blast in the show "Revolution", they would other wise die. Plus an anti EMP does exits and that is to protect the device with very dense materials, lead is an option but research and you'll find that tungsten is far more dense as the second densest material on earth, but EMPs are difficult to stop, because any connection would kill the device even if it had a wireless antenna, it is a very difficult topic to discuss, also the stuff i said may seem bullshit but it is all true, if you study hard and do a dense research you'll see it, finally in the matrix the EMP should kill everyone but miraculously they survive.
In order for an EMP blast to kill a new device first you need to know what kind of protection it has, the power supply circuits must be designed to filter and absorb large transient pulses of energy deriving from the EMP, therefore a normal sized laptop or computer would end up being 12-13 times larger in size, such devices only exist in military facilities which protect all kinds of important data from any kind of attack, they even place very powerful permanent magnets to direct the EMP to the devices in such a way that the energy is dispersed, plus that thing tha i mentioned earlier that it will automatically shut off the device when the EMP is about to occur is also used, your laptop, cell phone and any new electronic device used in our real world doesn't have that kind of protection, so i'll conclude my answer by saying that if you have a normal new device it will be affected and if you try to kill the devices in the military facilities, an EMP blast would not work, leaving the military people the only ones capable of still using electricity, this protection is so complicated that in an aircraft carrier (example) there is only one small room which is lead lined and everything only to protect the database of the ship, military info, satellite info and some US information, even the captain of the ship needs special access and he is monitored all the time, the room can only take a few people, this kind of protection is very complicated and the devices especially are very complicated and very expensive to build.
The final answer is yes, it is possible, if for example (to show dimensions) you set off a nuclear bomb 30 miles above the US continent directly in the middle, it would set off an EMP covering the whole state plus a bit of canada and parts of south america.