The instantaneous power p(t) in an AC circuit is given by which expression?

The instantaneous power p(t) in an AC circuit is given by which expression?

• A. p(t) = v(t)
• B. p(t) = i(t)
• C. p(t) = v(t) i(t)
• D. p(t) = V_rms I_rms cos φ

Answer: (C)

The rate at which energy is transferred in a circuit at each instant is the product of the instantaneous voltage and the instantaneous current. So the instantaneous power is p(t) = v(t) i(t). This reflects the idea that power is energy per unit time, and at any moment the energy flow depends on both the voltage driving the current and the current that results at that moment. In AC signals, both v(t) and i(t) vary with time and can have a phase difference, so multiplying them gives a time-varying p(t) that can be positive or negative, indicating absorption or delivery of energy by the element (as with reactive components). The other expressions don’t capture this instantaneous transfer. p(t) = v(t) would imply power equals voltage alone, which has the wrong units and ignores current. p(t) = i(t) likewise misses the driving voltage and has the wrong units. The form V_rms I_rms cos φ corresponds to the average (real) power over a cycle, not the instantaneous power, and it does not reflect how p(t) changes with time.

The rate at which energy is transferred in a circuit at each instant is the product of the instantaneous voltage and the instantaneous current. So the instantaneous power is p(t) = v(t) i(t). This reflects the idea that power is energy per unit time, and at any moment the energy flow depends on both the voltage driving the current and the current that results at that moment. In AC signals, both v(t) and i(t) vary with time and can have a phase difference, so multiplying them gives a time-varying p(t) that can be positive or negative, indicating absorption or delivery of energy by the element (as with reactive components).

The other expressions don’t capture this instantaneous transfer. p(t) = v(t) would imply power equals voltage alone, which has the wrong units and ignores current. p(t) = i(t) likewise misses the driving voltage and has the wrong units. The form V_rms I_rms cos φ corresponds to the average (real) power over a cycle, not the instantaneous power, and it does not reflect how p(t) changes with time.