Why is it so that for a signal to be an energy signal it must have power zero and for a power signal the energy value should be infinity ?
Reading between the lines of the question: -
Firstly a signal that posseses energy has the potential to do work - it can convert that energy into heat or just pass that energy on to something else. Energy isn't lost, it either remains "potential" energy or gets transferred to something else partially or wholly.
When energy is taken from an object or a component (such as an inductor or capacitor or spring or flywheel), the amount of energy taken divided by the time elapsed to take that energy is power. Over a long time period this is often called "average power"
Therefore, for a signal possessing energy to have zero power I guess you could say that it is not losing or gaining any energy i.e. it is in equilibrium.
By contrast, if something is giving off power and is still in energy equilibrium it must have infinite energy.
I've done the best I can to try and read between the lines of this question and if you want a better answer you'll have to try and explain the statements in your question.
Edit: some don't understand power and energy signals. I assume they were never undergrad EEs. I found this definition online:
There is a graphical illustration here: http://demonstrations.wolfram.com/EnergyAndPowerOfSignals/
But an energy signal has zero power, because energy is power integrated over all time. When you find the power in an energy signal, you have a finite energy divided by infinity. Thus zero.
For example, a non-rechargeable battery is an energy signal. It holds a finite amount of energy. It can supply some power only for a limited time, but if you compute the average power over your lifetime you will get a very small number.
A power signal is always adding some energy, so integrated over all time (to get energy) will give an infinite result.
For example, the sun is (an approximation of) a power signal. It radiates at a constant power. If you add the energy it gives off over your lifetime, you will get a very large number. For a better example, imagine a sun that exists for all time and never burns out. This sun would supply infinite energy when you add up its energy over all time.
Energy signals have values only in the limited time duration, a signal having only one square pulse is energy signal, A signal that decays exponentially has finite energy, so, it is also an energy signal, The power of an energy signal is zero, because of dividing finite energy by infinite time. the power signal is not limited in time, the energy of a power signal is infinite Thus, we use power (energy per given time) for power signal. in simple words energy is work and power is work per time.