Electric Power

🡑 Basics

General Power Definition

Power is the rate of energy consumed or produced. The general definition of power in equation form is:

p(t)=\frac{dw(t)}{dt}

Where:

p(t) = time function of power absorbed in watts

w(t) = time function of energy absorbed in joules

t = time in seconds

Electric Power Definition

One of many ways to transfer energy is through electric power. To express power from an electrical standpoint, let’s imagine electrons flowing through an object.

We can further expand \frac{dw(t)}{dt} into:

\frac{dw(t)}{dt}=\frac{dw(t)}{dQ(t)}\frac{dQ(t)}{dt}

Notice that:

\frac{dw(t)}{dQ(t)}=v(t) \frac{dQ(t)}{dt}=i(t)

Where:

Q(t) = time function of electrical charge flowing through an object in coulombs

v(t) = time function of voltage drop across an object in volts

i(t) = time function of current going through a load in amperes

Substituting voltage and current functions into the power equation, we can get the following electric power equation.

p(t) = \frac{dw(t)}{dt} = v(t) \times i(t)

Example

Power and Energy Practice

Find the current drawn when a 90 W light bulb is applied 12 V.

\begin{aligned} i(t) &= \frac{p(t)}{v(t)} \\ &= \frac{90\ watt}{12\ V} \\ &= 7.5\ A \end{aligned}