Are there any unsolved problems in Electrical Engineering?

Yup. Plenty.

How to increase, maximize trhe energy density of a storage cell.

How to improve the efficiency of a solar cell.

How to make smaller transistors and wires in a chip without the quantum cross-talk.

How to build a computer using Photo-Refraction.
must be lot many. thedoctoral thesis of graduating Ph.D. studentsand research papers publishet in Journals are based on suck unresolved problems.
One could say that there will always be unsolved problems in electrical engineering. As long as there is invention and new technology, there will be unsolved problems in EE.

An example of a current problem: Wifi, wireless internet LANs, and wireless connectivity is suffering because of low power requirements of the transmitters. Some EEs will come along someday, soon, and solve these problems (and it's not just a matter of increasing transmitter power).

Unsolved problems? Yes. Here's one: I need a bi-directional sense circuit at the secondary of a current-sense transformer for a PWM using less than $5.00 of parts. Can you solve this for me?

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