Foundations — Define resistance and the ohm

Before you can trust the formula $R=V/I$, you must be able to read every letter and symbol in it as a picture, not a squiggle. This page builds each one from nothing, in the order they depend on each other. Nothing here assumes you have seen the parent note — it feeds the parent note Define resistance and the ohm.

Symbol 0 — Electric charge, $Q$

The picture: imagine a bucket holding little blue marbles. Each marble is a packet of charge. $Q$ is how many marbles you have — not how fast they move, just the count (measured in coulombs).

Why the topic needs it: current and voltage are both defined using charge. If you don't know what $Q$ is, the definitions below are just letters. Charge is the raw stuff that flows. See Conductors and Insulators for what lets charge move or blocks it.

Symbol 1 — Time, $t$, and the idea of "per second"

The picture: a stopwatch ticking. Every time it ticks one second, we count how many charge-marbles crossed a line.

Why "per second" matters: "10 marbles crossed" means nothing until you say over how long. Ten marbles in one second is a gush; ten marbles in an hour is a trickle. The word per (the slash in $Q/t$) means "for every one second". That single idea powers the definition of current next.

Symbol 2 — Electric current, $I$

Why divide $Q$ by $t$? We choose division because we want a rate, and "how much per how long" is exactly what division answers. If $6\text{C}$ pass in $2\text{s}$, then $I=6/2=3\text{A}$ — three coulombs every second.

The picture: stand at a bridge over a river of marbles. Current is how many marbles float under the bridge each second. Widen the flow → more marbles/second → bigger $I$.

Symbol 3 — Energy, $E$

The picture: a wound-up spring. The tighter it's wound, the more joules it can spend shoving something. In a circuit, energy is what gets spent to drag charge through a component.

Why the topic needs it: voltage (next) is defined as energy shared out per unit of charge. Without $E$ we cannot say what the "push" actually is.

Symbol 4 — Voltage, $V$

Why divide $E$ by $Q$? Again we pick division to make a "per" quantity: joules per coulomb. This tells us how much energy each single coulomb is given to make its trip — the strength of the push, independent of how many coulombs there are.

The picture: the height of a waterfall. A tall fall gives each drop a big shove; a low fall barely nudges it. Voltage is that height — the shove per drop, not the number of drops. Dive deeper in Voltage and Potential Difference.

Symbol 5 — Proportionality, the "$\propto$" sign

The picture: a straight line through the origin $(0,0)$ on a graph. No curve, no bend — a perfectly straight ramp. The steepness of that ramp is a fixed number.

Why the topic needs it: the whole idea of resistance rests on the experimental fact that for a metal at fixed temperature, $V$ and $I$ rise in lockstep — a straight line. This is Ohm's Law. A proportionality with a fixed steepness is begging to be written as an equation with a constant, which is our final symbol.

Symbol 6 — The constant of proportionality, $R$

Why introduce a constant at all? Because "$V\propto I$" only says they rise together — it doesn't say by how much. The constant $R$ is the "how much": the amount of push needed per unit of flow. That is the definition of resistance.

The picture: on a $V$-vs-$I$ graph, $R$ is the steepness of the line. A steep line means you spend lots of volts for each amp → high resistance. A shallow line means little push per amp → low resistance. (Careful: the parent note plots $I$ vs $V$, where the slope is the reciprocal $1/R$ — same physics, axes swapped.)

Why $\text{J}\cdot \text{s}/{\text{C}}^2$? Substitute $\text{V}=\text{J/C}$ and $\text{A}=\text{C/s}$ and simplify the fraction — the coulombs multiply to ${\text{C}}^2$ in the bottom, the second moves up top. This shows the ohm is not a new fundamental thing; it is charge, energy, and time recombined. Resistance depends on what the path is made of and its shape — see Resistivity and Resistance of a Wire.

How every symbol feeds the topic

Read it top-down: charge and time make current; energy and charge make voltage; the experimental fact that voltage and current stay proportional forces a constant, and that constant is resistance, measured in ohms.

Where the numbers land (a full-circle check)

Note this connects onward: energy spent per second is power, the root of Power Dissipation in Resistors.

Equipment checklist

Cover the right side and test yourself — you are ready for the parent topic only if each is instant.

Connections

• Define resistance and the ohm — the parent topic these foundations feed into.
• Electric Current — the meaning of $I=Q/t$ in full.
• Voltage and Potential Difference — the meaning of $V=E/Q$ in full.
• Ohm's Law — where $V\propto I$ comes from and its limits.
• Conductors and Insulators — what lets charge move or blocks it.
• Resistivity and Resistance of a Wire — what sets the size of $R$.
• Power Dissipation in Resistors — energy per second, the next step up.
• Hinglish version — same ideas in Hinglish.