Electric potential and potential difference

Plug in a torch bulb and current flows the instant the circuit closes — but why does charge move at all? Something has to do work on it, the way a pump does work to push water through a pipe. That "something" is the cell, and the work it does per unit charge is called potential difference. This is the second building block of the CBSE Class 10 chapter "Electricity," coming right after electric current, and it sets up everything that follows: Ohm's law links current and potential difference through resistance, and every circuit numerical from here on leans on the formula $V = W/Q$ . This article defines potential difference precisely, explains how a cell maintains it and how a voltmeter measures it, and walks through the arithmetic with worked numbers you can reuse in your own problems.

The core insight

Potential difference $V = W/Q$ is the work done per unit charge by a cell in driving current through a circuit, measured in volts with a voltmeter connected in parallel.

The core idea

Current tells us how much charge flows and how fast; potential difference tells us how much work is done to move that charge between two points. It is the "electrical push" behind the flow.

Definition. The electric potential difference $V$ between two points is the work done $W$ in moving a unit positive charge $Q$ from one point to the other:

V = \dfrac{W}{Q}

where: $W$ is the work done, in joules (J); $Q$ is the charge moved, in coulombs (C); and $V$ is the potential difference, in volts (V).

The unit. One volt is the potential difference between two points when one joule of work is done in moving one coulomb of charge between them:

1\ \text{V} = \dfrac{1\ \text{J}}{1\ \text{C}}

The volt is named after Alessandro Volta, who built the first chemical cell.

The source. A cell or battery is a source of potential difference. Through the chemical reactions inside it, it does work on charges and maintains a potential difference between its two terminals. That maintained push is what drives current through any external circuit connected across it — the cell does not create charge, it continuously does work on the charge already present in the closed loop, pushing it around again and again.

The measuring instrument. Potential difference is measured with a voltmeter, always connected in parallel across the component (or the two points) being measured — never in series, unlike an ammeter. The reason is that a voltmeter must compare the "electrical push" at two points without diverting the current path itself, so it sits alongside the component, not inside its path.

Figure

A simple circuit with a cell an ammeter and a bulb in series and a voltmeter connected in parallel across the bulb

A note on wording. In a Class 10 context, "voltage" and "potential difference" mean the same thing, and both are always measured between two points — it never makes sense to speak of "the potential difference of a single point" without a second reference point.

Derivation ARearranging V = W/Q for work and charge

The goal is to show, with nothing more than the algebra of rearranging a defining equation, that the single relation $V = W/Q$ can be solved for any one of its three quantities once the other two are known — which is exactly what every potential-difference numerical in this chapter asks you to do, whether the unknown is the work done, the charge moved, or the potential difference itself.

Step 1. Start from the definition. Potential difference is work done per unit charge: $V = \dfrac{W}{Q}$ . This single line is the entire content of the concept — everything else is bookkeeping of units.

Step 2. Solve for work done. Multiplying both sides by $Q$ gives $W = V \times Q$ : the work done in moving a charge $Q$ through a potential difference $V$ is simply their product, in joules when $V$ is in volts and $Q$ is in coulombs.

Step 3. Solve for charge moved. Dividing both sides of $W = VQ$ by $V$ gives $Q = \dfrac{W}{V}$ : the charge moved by a given amount of work through a known potential difference.

Step 4. Keep the three forms straight: $V = W/Q$ to find the potential difference, $W = VQ$ to find work done, and $Q = W/V$ to find charge moved — one relation, three rearrangements, and every quantity must be in SI units (joules, coulombs, volts) before you plug in numbers.

Worked example

A source does 600 J of work in moving 50 C of charge through a circuit. (a) Find the potential difference across the source. (b) Using that potential difference, find how much work the same source would do in moving a smaller charge of 4 C.

Step 1. Find the potential difference. Given $W = 600\ \text{J}$ and $Q = 50\ \text{C}$ , use $V = \dfrac{W}{Q}$ :

V = \dfrac{600\ \text{J}}{50\ \text{C}} = 12\ \text{V}

This is a typical car-battery rating.

Step 2. Use this potential difference for the new charge. Since the source maintains the same $V = 12\ \text{V}$ across its terminals, moving a charge of $Q = 4\ \text{C}$ needs work $W = V \times Q$ :

W = 12\ \text{V} \times 4\ \text{C} = 48\ \text{J}

Answer: the potential difference across the source is 12 V, and moving 4 C of charge through it does 48 J of work. Note that this only tells us the push the source maintains; the actual current that flows also depends on the resistance in the circuit — the subject of Ohm's law, next.

Common traps

Confusing an ammeter's series connection with a voltmeter's parallel connection — a voltmeter always sits across the component being measured.
Treating "potential" and "potential difference" as needing no reference point — only the difference between two points is meaningful and measurable in this syllabus.
Mixing up units in $V = W/Q$ — work must be in joules and charge in coulombs, not any everyday unit like mAh.
Assuming a higher-rated cell (say 9 V) always drives more current — current also depends on the circuit's resistance, which is where Ohm's law comes in.

Ask the tutor: Want to see how potential difference and current combine through Ohm's law, or need another worked numerical on $V = W/Q$ ?

Why is a voltmeter connected in parallel and not in series like an ammeter?

An ammeter measures the current actually flowing through a branch, so it must be part of that branch — connected in series, in the current's own path. A voltmeter instead compares the "electrical push," the work done per unit charge, between two points, so it needs to sit alongside the component, sampling both ends without diverting the current that flows through the component itself. Connecting a voltmeter in series would break the circuit and its high resistance would stop the flow almost entirely.

Is voltage the same thing as potential difference?

Yes, in the Class 10 syllabus "voltage" is simply the everyday name for potential difference — the two words describe the same physical quantity, work done per unit charge, and are used interchangeably. What matters is remembering that it is always a quantity measured between two points; there is no such thing as the voltage or potential difference "at" a single point without saying what it is being compared to.

Does a higher-voltage cell always push more current through a circuit?

Not necessarily. A cell's rated potential difference tells you the work it does per unit charge, which is the "push" available, but the actual current that flows also depends on the resistance of the circuit it drives, through Ohm's law. A 9 V cell connected across a very high resistance can drive less current than a 1.5 V cell connected across a very low resistance. Potential difference alone never fixes the current — resistance is the other half of the story.

Electric potential and potential difference

The core idea

Worked example

Common traps

Before this

Where this leads