Foundations — Calculate electrical power (P = VI, P = I²R)

This page builds every symbol used by the power topic from absolute zero. Nothing is assumed. Each item gives: what it means in plain words, the picture it draws, and why the topic can't work without it. Read top to bottom — each one is a brick for the next.

0. The stage: what is a circuit?

Before any symbol, picture the thing everything lives on.

A circuit is a closed loop of conducting material (wire) with a source that pushes and a component that resists. Tiny charged particles — think of them as marbles — are shoved around the loop by the source and rub against the component, giving up energy as heat or light.

1. Charge — the "stuff" that moves ($Q$)

The picture: a bucket holding some marbles. $Q$ is simply "how full the bucket is."

Why the topic needs it: Energy is delivered by moving charge. You cannot talk about "energy per charge" (voltage) or "charge per second" (current) until you have named the charge itself. $Q$ is the raw ingredient both of the topic's key definitions are built from.

2. Time — the pace-setter ($t$)

The picture: a stopwatch ticking beside the circuit.

Why the topic needs it: Power is a rate — energy per second. Current is a rate — charge per second. Both words "power" and "current" are meaningless without a clock. This is also the number learners most often get wrong (using minutes or hours instead of seconds), so anchor it now: the topic's seconds are always seconds.

3. Energy — the thing being delivered ($E$) and the joule

The picture: a stored spring, or the "whee!" a kid collects sliding down. Energy is what gets spent when charge moves through the drop.

Why the topic needs it: Power is literally energy divided by time. Without energy there is nothing whose rate we are measuring. $E$ sits at the heart of the very first definition on the parent page.

4. Rate — the idea of "per second" (division as a picture)

Before we combine anything, make sure one piece of notation is crystal clear: the fraction bar meaning "per."

Why the topic needs it: Every formula here — $P=E/t$, $V=E/Q$, $I=Q/t$ — is a "per" statement. If you can read a fraction bar as "steepness of a line," you can read the whole topic.

5. Voltage — energy handed to each marble ($V$)

The picture: the height of the water slide. A tall slide gives each kid a big drop (lots of joules each); a short slide gives each kid only a little. Voltage says nothing about how many kids — only how big each one's drop is.

WHY this tool and not just "energy"? We split energy into "per charge" (voltage) and "how much charge" separately, because in a circuit these two are controlled by different things — the battery sets the height, the wire/component sets the flow. Keeping them apart lets us multiply them back later ($E=VQ$) to recover energy. That rearrangement is step 1 of the parent's derivation.

6. Current — how many marbles pass per second ($I$)

The picture: stand at the bottom of the slide and count kids arriving each second. Many kids per second = big current. Notice it says nothing about the height — only the flow rate.

WHY the symbol is $I$, not $C$: historical (from French intensité), but treat it as a fixed name. The key is the rearrangement $Q=It$: "total charge = flow rate × how long it flowed." That is step 2 of the parent's derivation.

7. Putting them together: why $P=VI$

Now every symbol is earned, watch the parent's headline formula assemble itself.

$P=\frac{E}{t}=\frac{VQ}{t}=\frac{V(It)}{t}=VI$

WHAT we did: replaced $E$ with $VQ$ (from voltage) and $Q$ with $It$ (from current), then the $t$'s cancelled. WHY: to express power using the two things we can actually measure with a meter — volts and amps. WHAT IT LOOKS LIKE: a tall slide (big $V$) crowded with kids (big $I$) makes enormous fun-per-second (big $P$).

8. Resistance and Ohm's law — the rough slide ($R$)

The picture: a rough slide. The rougher it is (bigger $R$), the harder it is to push kids down — so for a given push (voltage) fewer kids flow, or to force more kids you need a bigger push. That tug-of-war is $V=IR$.

WHY the topic needs it: Often you don't know both $V$ and $I$ — you know one plus $R$. Ohm's law lets you swap one for the other, producing $P=I^{2}R$ (replace $V$) and $P=V^2/R$ (replace $I$). Every alternate power formula is $P=VI$ with Ohm's law substituted in.

9. Why the square in $I^{2}R$ — a picture of "two things at once"

Why this matters for Hardware: heat is the enemy. Because loss is $I^{2}R$, engineers keep current low and resistance low (thick wires) — see Heat Dissipation and Cooling. A small rise in current is a big rise in heat.

The prerequisite map

Equipment checklist

Cover the right side and test yourself. If any answer is fuzzy, re-read that section before the parent page.

Connections

• 1.1.07 Calculate electrical power (P = VI, P = I²R) (Hinglish) — the parent topic this page prepares you for.
• Voltage and Potential Difference — the $V=E/Q$ brick.
• Electric Current — the $I=Q/t$ brick.
• Energy and the Joule — the $E$ and joule brick.
• Ohm's Law (V = IR) — the bridge to $I^{2}R$ and $V^2/R$.
• Resistors and Power Ratings — where $R$ and power limits meet.
• Heat Dissipation and Cooling — why the $I^{2}R$ square dominates hardware design.