Noesis
1.1.3 · D5Electricity & Charge Basics

Question bank — Define voltage (potential difference) and its units

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This page assumes only the parent definition: voltage is $V = W/q$, work per unit charge, measured in volts (joules per coulomb). Every term you need is built there.

True or false — justify

Voltage can exist at a single isolated point with no other point mentioned.
False — voltage is a difference between two points; a lone "voltage" is silently measured against a reference (ground, 0 V), so a second point is always hiding in the statement.
A 9 V battery and a 1.5 V battery both move 1 C — the 9 V battery does more work on that coulomb.
True — , so for the same C the 9 V battery delivers 9 J while the 1.5 V one delivers 1.5 J; higher voltage means a taller "hill" per coulomb.
If you double the charge moved between two fixed points, the voltage between them doubles.
False — voltage is energy per charge; doubling doubles the work too, so is unchanged. The hill height does not depend on how much you carry.
Two points can have a large voltage between them yet have zero current flowing.
True — voltage is the push (potential difference); current needs a conducting path. A 9 V battery sitting on a table has 9 V across its terminals and 0 A until you connect something (see Ohm's Law V=IR).
Zero volts between two points means the two points are physically the same place.
False — it means they are at the same potential (same energy-per-charge), like two spots at the same height on a hill; they can be far apart with a wire between them.
Voltage has units of joules because it measures energy.
False — a volt is joules per coulomb (J/C), not joules; shows a volt becomes energy only after multiplying by a charge.
Reversing which point you call and which you call flips the sign of the voltage.
True — , because the work to go from to is the negative of the work to go from to ; the magnitude of the "height difference" is the same, only the direction flips.
Voltage flows through a wire from the battery to the bulb.
False — charge (current) flows; voltage is a difference between two points and does not travel. Say "voltage across the bulb," never "through."

Spot the error

"The multimeter reads 5 V on this wire, so this wire has a voltage of exactly 5 V, no reference needed."
The error: the reading is relative to the meter's black (reference) probe. Move that probe elsewhere and the number changes — 5 V is always 5 V relative to something.
"It takes 6 J to move 2 C between the points, so the voltage is 12 V."
The error: they multiplied instead of dividing. Voltage is energy per charge, V. Multiplying gives back joules, not volts.
"Volts and joules are interchangeable since both appear in ."
The error: they differ by a factor of charge. In , the (coulombs) is exactly what converts a volt into a joule; drop it and the units don't match.
"There's no voltage across the light bulb because current is passing through it."
The error: current flowing requires a voltage across the bulb to push it (see Ohm's Law V=IR, ). Current through a resistor is evidence of, not the opposite of, a voltage across it.
"The battery gives 240 J to every coulomb because it delivered 240 J total."
The error: 240 J is the total over all the charge moved. Per coulomb it's ; if 20 C moved, each coulomb got J, i.e. 12 V.
"Voltage is measured in volts, and current is also a kind of voltage measured in amps."
The error: current is charge-per-time (, amps), a completely different quantity from voltage (energy-per-charge, volts). They combine in $P = VI$ but are not the same thing.

Why questions

Why do we divide the work by the charge instead of just quoting the total work done?
Dividing out describes the hill itself (a property of the two points), independent of how much charge you happen to carry across it — that's what makes voltage reusable for any charge.
Why does a single point need a "ground" before we can say it has a voltage?
Because energy-per-charge only has meaning as a difference between two positions on the hill; picking ground fixes one point at 0 V so every other point gets a defined number relative to it.
Why can the electric field be nonzero somewhere yet the voltage between two points be zero?
Voltage is the net work per charge along a path; if the field pushes you uphill then equally downhill, the net work cancels to zero even though the field was present the whole way (see Electric field and potential energy).
Why is , and not , the right way to combine voltage and current?
Power is energy per second: . The charge per second () and the energy per charge () multiply because each carries a different "per" that must chain together (see Batteries and EMF).
Why does raising the voltage of a source make charges "want to move" harder?
Higher voltage means more energy delivered per coulomb — a taller electric hill — so each charge is pushed with more force, analogous to a taller water slide sending water down faster.
Why is voltage sometimes called EMF for a battery but "potential difference" for a resistor?
EMF is the voltage a source supplies by doing work to lift charge; potential difference is the voltage dropped across a component as charge falls back down (see Batteries and EMF). Same units, opposite roles.

Edge cases

What is the voltage between a point and itself?
Exactly 0 V — moving charge from a point back to the same point requires zero net work, so and .
If (no charge moved), is the voltage undefined because divides by zero?
No — voltage is a property of the two points, defined as the limiting ratio of work to charge for any test charge. With no charge you simply do no work ( too); the hill's height still exists, we just aren't using it.
What voltage does an ideal wire (zero resistance) have across its two ends when current flows?
Zero — with no resistance there is no "hill" to climb (), so both ends sit at the same potential even though charge is flowing through (see Ohm's Law V=IR).
Can voltage be negative, and what does a negative value mean?
Yes — just means point is lower on the hill than , so moving positive charge from to releases energy instead of requiring it; the sign encodes direction, not an error.
Two batteries face each other, 9 V and 9 V, terminals opposing. What is the net voltage across the pair?
Zero — the two equal, opposing hills cancel, so no net push is available and (ideally) no current flows, just like two identical slides facing uphill against each other.
If you move a charge in a full loop back to its start, what is the total voltage it experienced?
Zero net voltage around the loop — every bit of energy gained climbing is given back descending, since potential depends only on position, not on the path taken.
Recall One-line summary of the traps

Voltage is a difference (needs two points + a reference), it is per charge (not total energy, not joules), it does not flow (charge does), and its sign just says which point is higher. Master those four and every trap above collapses.

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