Foundations — Define energy (joules) vs power (watts)

This page assumes you know nothing. We will name every letter, symbol, and unit the parent note throws at you, draw the picture behind it, and say why the topic can't live without it. Read top to bottom — each item is built only from the ones above it.

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0 — What a "symbol" even is here

In physics we use short letters to stand for measured amounts. The letter is just a nickname. The whole game is: know what real-world quantity the nickname points to, and what unit it is measured in. A unit is the agreed "one chunk" we count in — like saying "3 apples", the apple is the unit.

We will meet these nicknames on this page:

Symbol	Nickname for...	Unit
$E$ or $W$	energy	joule, $\text{J}$
$P$	power	watt, $\text{W}$
$t$	time	second, $\text{s}$
$F$	force	newton, $\text{N}$
$d$	distance	metre, $\text{m}$
$Q$	electric charge	coulomb, $\text{C}$
$V$	voltage	volt, $\text{V}$
$I$	current	ampere, $\text{A}$
$\Delta$	"a change in..."	—
$\frac{d}{dt}$	"rate of change per second"	—

Let's earn each one.

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1 — Force ($F$) and distance ($d$): the raw ingredients of work

Why do we need these two first? Because the whole idea of energy is born from them. Look at the figure: a push that goes nowhere does nothing; a push that moves something a long way does a lot.

The picture: an amber arrow (the force) shoved along a white track for a distance. The "amount of effort spent" is the arrow's strength times how far it dragged.

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2 — Energy ($E$) and the joule ($\text{J}$)

The picture: energy is the shaded area — force (height) times distance (width). One joule is one little rectangle. Energy is a pile you count; it has no clock inside it. (See Work-energy theorem (mechanics) for the mechanics version of this same rectangle.)

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3 — Time ($t$) and the second ($\text{s}$): the bridge

Why does the topic need $t$ so badly? Because energy alone can't tell you if a wire melts. The same pile of joules dumped in a microsecond behaves totally differently from the same pile leaked out over a night. Time is the knob that turns one into the other.

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4 — Power ($P$) and the watt ($\text{W}$)

The picture: think of joules dropping into a bucket. Power = how many drops per second. Below, the same total (same number of joules) arrives at two different speeds.

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5 — The symbols $\Delta$ and $\frac{d}{dt}$: reading "rate"

The parent note writes $P=\frac{\Delta E}{\Delta t}$ and then $P=\frac{dE}{dt}$. These look scary — they are just careful ways of writing "per".

Why does the topic reach for this tool and not just plain division? Because real power isn't always steady — a flash spikes, a kettle holds flat. The $\frac{d}{dt}$ notation is the only honest way to say "the rate at this exact instant." When power is steady, it collapses back to ordinary division $E/t$, and you never need the fancy version.

The picture: the slope (steepness) of an energy-vs-time graph is the power. Steep = fast = high power. Flat = nothing flowing.

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6 — The electrical trio: charge $Q$, voltage $V$, current $I$

The parent's grand finale is $P=IV$. To read it you need three more nicknames, each fully defined in its own linked note.

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7 — The kilowatt-hour: a unit made of two others

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Prerequisite map

Read it as a river: force and distance flow together into energy; energy divided by time makes power; charge and voltage rebuild energy the electrical way; that feeds $P=IV$; and power stretched over hours becomes the kilowatt-hour on your bill.

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Equipment checklist

Recall Am I ready? Cover the right side and answer.

What is a joule, in force-and-distance words? ::: The work done when a $1\text{N}$ force moves something $1\text{m}$; $1\text{J}=1\text{N}\cdot \text{m}$. What is a watt, in energy-and-time words? ::: One joule delivered every second; $1\text{W}=1\text{J/s}$. What does the symbol $t$ contribute to the whole topic? ::: It is the bridge that turns a total (energy) into a rate (power), via $P=E/t$. What does $\Delta E/\Delta t$ mean in plain words? ::: Energy gained divided by the time it took — the average power over that stretch. What does $dE/dt$ mean and why use it? ::: The rate of energy transfer at a single instant; needed when the rate isn't steady. What is charge $Q$ and its unit? ::: The electric "stuff" that flows; measured in coulombs ($\text{C}$). What is voltage $V$ in energy terms? ::: Joules of energy carried per coulomb of charge; $V=\text{J}/\text{C}$. What is current $I$ in charge terms? ::: Coulombs of charge flowing per second; $I=Q/t$, in amperes ($\text{A}$). Rebuild $P=IV$ from definitions. ::: $P=E/t=QV/t=(Q/t)V=IV$. Is a kilowatt-hour power or energy? ::: Energy — it equals power $\times$ time = $3.6\text{MJ}$.

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Connections

• Define energy (joules) vs power (watts) — the parent topic this page equips you for
• Voltage as energy per charge (V = J/C)
• Current as charge per second (I = Q/t)
• Electric charge and the coulomb
• Ohm's Law and P = I²R = V²/R
• Kilowatt-hour and electricity billing
• Work-energy theorem (mechanics)