The total energy of a signal is defined as:

• A. The integral over time of power.
• B. The product of time and energy.
• C. The maximum power value.
• D. The integral of voltage over time.

Answer: (A)

Total energy is found by integrating the instantaneous power over time. Power tells you how fast energy is being delivered at each moment, so integrating p(t) across all time gives the total energy that the signal can deliver. For a signal viewed as a voltage across a reference impedance, instantaneous power is p(t) = v(t)i(t); with a unit impedance, this becomes p(t) = v(t)^2, so the energy is E = ∫{-∞}^{∞} p(t) dt = ∫{-∞}^{∞} |x(t)|^2 dt. This makes the integral of power over time the correct definition of total energy.

The other ideas don’t match energy units: multiplying energy by time isn’t meaningful for total energy; maximum power is just a peak value and does not account for the whole duration; and integrating voltage over time gives volts-seconds, not energy unless you include impedance to convert voltage to power.