Define resistance and the ohm: Question bank — Hardware deep dive

Before we start, three plain-word reminders so every symbol below is already earned:

$V$ (voltage) — the energy each unit of charge carries as a "push". See Voltage and Potential Difference.
$I$ (current) — how much charge flows past a point each second. See Electric Current.
$R$ (resistance) — how strongly the path fights that flow, defined as $R = \frac{V}{I}$ , measured in ohms ( $Ω$ ). See Ohm's Law.

True or false — justify

True or false: If you double the voltage across a fixed resistor, its resistance doubles.

False. Doubling

V

doubles

I

too, so the ratio

R = V / I

is unchanged; resistance is a property of the component, not of the push you apply.

True or false: A wire with zero resistance would still limit current.

False. With

R = 0

I = V / R

blows up (no limit from the wire itself) — this is why "ideal wires" carry current freely and why real short-circuits draw huge currents.

True or false: The ohm is a fundamental SI unit like the metre.

False. The ohm is a derived unit:

1 Ω = 1 V/A = 1 J\cdots/C^{2}

, built from volts and amperes.

True or false: On an

I

-vs-

V

graph, a steeper line means a larger resistance.

False. The slope equals

I / V = 1/ R

, so a steeper line means a smaller

R

— current flows more easily for each volt.

True or false: An insulator has infinite resistance and a perfect conductor has zero resistance.

True as idealisations. Real materials sit between these extremes; see Conductors and Insulators — but "infinite" and "zero" are the limiting cases the definition

R = V / I

points to.

True or false: If no current flows through a resistor, its resistance must be zero.

False. Zero current usually means zero applied voltage;

R

is the ratio

V / I

, a fixed property that exists whether or not anything is flowing.

True or false: Two components with the same resistance always have the same voltage across them.

False. Same

R

only fixes the ratio

V / I

; the actual voltage depends on how much current the circuit pushes through each one.

True or false: Resistance and voltage are the same kind of quantity because both appear in

V = I R

False. Volts measure energy per charge (the push); ohms measure push per unit resulting flow (the opposition). Different physical meanings, different units.

Spot the error

"Since

R = V / I

, a component with more voltage across it has more resistance." — what's wrong?

The error treats

R

as depending on

V

alone. Raising

V

raises

I

in step, so the ratio stays fixed; you can't judge

R

from

V

without knowing

I

too.

"The slope of the

I

–

V

line is the resistance, so I read

R

straight off the graph." — what's wrong?

Slope

= I / V = 1/ R

, the reciprocal of resistance. To get

R

you take

1/ slope

(or read one point and compute

V / I

"1 volt = 1 ohm because both measure how strong the electricity is." — what's wrong?

A volt is energy per charge (J/C); an ohm is V/A. They are not equal and not even the same dimension — one is the push, the other is opposition to flow.

R = V / I

, so if I make

I

tiny by using a small voltage, the resistance becomes huge." — what's wrong?

Shrinking

V

shrinks

I

proportionally, so the ratio

V / I

holds steady.

R

only changes if the material, geometry, or temperature changes — not by turning the supply down.

"A thick wire and a thin wire of the same metal must have the same resistance since they're the same material." — what's wrong?

Material is only one factor. Resistance also depends on length and cross-sectional area — the thin wire resists more. See Resistivity and Resistance of a Wire.

"Ohm's law

V = I R

works for every electrical component." — what's wrong?

It only holds for ohmic components (constant

R

, straight

I

–

V

line) at fixed temperature. Filament lamps, diodes and heated wires curve, so their

R

isn't a single constant.

Why questions

Why did engineers define resistance as a ratio

V / I

rather than just

V

or just

I

Because experiments showed that for a fixed wire the ratio

V / I

stayed constant even as

V

and

I

changed together — that stubborn constant is the property worth naming.

Why is one ohm defined using exactly 1 volt and 1 ampere?

It anchors the derived unit to already-defined units:

1 Ω

is the resistance that lets 1 V drive exactly 1 A, so the definition is measurable and reproducible.

Why does a low-resistance path draw more current for the same voltage?

From

I = V / R

, dividing the same push by a smaller opposition yields a larger flow — less "fighting back" means more charge per second gets through.

Why can we treat

R

as constant for a metal at fixed temperature but not when it heats up?

Ohm's law's constant-

R

behaviour assumes stable conditions; heating jostles the atoms more, obstructing electrons, so

R

rises and the

I

–

V

line bends.

Why is the ohm called a derived unit and what does that reveal about resistance?

Because it's built from volts and amperes (

1 Ω = 1 V/A

), showing resistance isn't a standalone quantity but a relationship between push and flow.

Edge cases

What is the resistance of a component when both

V = 0

and

I = 0

The ratio

0/0

is undefined from that single point, but

R

is still a definite property — read it from any non-zero

(V, I)

pair or the graph's slope, where

R = 1/ slope

What happens to

I = V / R

R \to 0

(an ideal short) with

V

fixed?

The current grows without bound (

I \to \infty

), which is why real short-circuits draw dangerously large currents limited only by the rest of the circuit.

What happens to

I = V / R

R \to \infty

(an ideal insulator) with

V

fixed?

The current shrinks toward zero — a perfect insulator lets essentially no charge through no matter how hard you push.

At the exact origin of the

I

–

V

graph, is the resistance zero because the line passes through

(0, 0)

No — passing through the origin just means zero current at zero voltage. The resistance is set by the slope everywhere on the line, and

R = 1/ slope

stays the same non-zero value.

If a real filament lamp's

I

–

V

curve bends, can we still quote "the" resistance?

Only at a specific point:

R = V / I

at that operating point. Because the curve isn't a single straight line,

R

isn't one fixed number — it grows as the filament heats. This ties back to Power Dissipation in Resistors, where heating changes behaviour.

Connections

Ohm's Law — the $V = I R$ line these traps probe.
Voltage and Potential Difference — the numerator's true meaning.
Electric Current — the denominator's true meaning.
Resistivity and Resistance of a Wire — why geometry, not just material, sets $R$ .
Conductors and Insulators — the zero/infinite- $R$ limiting cases.
Power Dissipation in Resistors — heating and non-ohmic behaviour.