The power is defined as rate at which the work is performed or the energy is converted. If the symbol ΔW is the amount of the work performed during any period of time of the duration Δt, then the average power Pavgover that period will be given by the formula

P_\mathrm{avg} = \frac{\Delta W}{\Delta t}\,.

It is overall the average amount of the work done or the energy converted per unit of the time. The average power is generally called power.

The instantaneous power is the limiting value of average power as time interval Δt tends to zero.

P = \lim _{\Delta t\rightarrow 0} P_\mathrm{avg} = \lim _{\Delta t\rightarrow 0} \frac{\Delta W}{\Delta t} =  \frac{dW}{dt}\,.

In case of the constant power P, amount of the work performed during any period of duration T is given by formula:

W = PT\,.

In context of the energy conversion it is very easy to use symbol E rather than symbol W.

Instantaneous Power

The instantaneous electrical power P is defined as the product of both the instantaneous current and the instantaneous voltage

            P(t) = I (t) . V(t)


P(t) is the instantaneous power. It is measured in watts or the joules per second.

V(t) is defined as the potential difference or the voltage drop across the component, measured in the volts.

I(t) is the current through the component. It is measured in the amperes.

If the component is a resistor with the time-invariant voltage to the current ratio, then the power is formulated as:


Here R is the resistance in the circuit which is measured in the ohms. R is the ratio of the voltage to the current. R is defined as R = V / I

The measuring unit of power is the energy divided by the time. Unit of the power is also the wattdenoted by symbol W, and it is equal to the one joule per second. Other measuring units of the power include >ergs per second (erg/s), >horsepower (hp). One horsepower is equal to  746 watts.

In the DC circuits, the instantaneous electric power in an AC circuit is given by P=VI similarly in the AC circuits where V and I are the instantaneous voltage and current. If there is a phase difference occurs in the applied voltage and the current so the instantaneous power is given by

                             V =

                              I = 

                 = sin ω t cos Ɵ – cos ωt sin Ɵ






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