Voltage Formula

The Formula

V = \frac{W}{Q} where W is energy (work) and Q is charge.

When to use: Voltage is like water pressure — it's the 'push' that drives current through a circuit.

Quick Example

A AA battery provides 1.5 V. A wall outlet provides 120 V (or 230 V in many countries). That's why outlets are more dangerous.

Notation

V is voltage in volts (V = J/C), W is work or energy in joules, Q is charge in coulombs, \vec{E} is the electric field, and d\vec{l} is an infinitesimal path element.

What This Formula Means

The difference in electric potential energy per unit charge between two points. Measured in volts (V).

Voltage is like water pressure — it's the 'push' that drives current through a circuit.

Formal View

Voltage (potential difference) between two points is V = \frac{W}{Q} = -\int_A^B \vec{E} \cdot d\vec{l}, where W is the work done per charge Q. In circuits, Kirchhoff's voltage law states \sum V = 0 around any closed loop.

Worked Examples

Example 1

easy
A battery does 24 \text{ J} of work to move 6 \text{ C} of charge. What is the voltage of the battery?

Solution

  1. 1
    Voltage is work done per unit charge: V = \frac{W}{Q}.
  2. 2
    Substitute the values: V = \frac{24}{6}.
  3. 3
    V = 4 \text{ V}

Answer

V = 4 \text{ V}
Voltage (potential difference) is the energy transferred per coulomb of charge. A higher voltage means more energy per charge, driving more current through a circuit.

Example 2

medium
A 12 \text{ V} battery drives a current of 2 \text{ A} for 30 \text{ s}. How much energy does it supply?

Common Mistakes

  • Saying 'the voltage through a component' — voltage is across (between two points), not through; current flows through components.
  • Thinking voltage is used up as current flows — voltage drops across each component, but the total drop around a loop equals the source voltage (Kirchhoff's voltage law).
  • Confusing EMF (the energy supplied per coulomb by a source) with terminal voltage (which is lower due to internal resistance).

Why This Formula Matters

Without voltage, there's no current — voltage is the driving force of every circuit.

Frequently Asked Questions

What is the Voltage formula?

The difference in electric potential energy per unit charge between two points. Measured in volts (V).

How do you use the Voltage formula?

Voltage is like water pressure — it's the 'push' that drives current through a circuit.

What do the symbols mean in the Voltage formula?

V is voltage in volts (V = J/C), W is work or energy in joules, Q is charge in coulombs, \vec{E} is the electric field, and d\vec{l} is an infinitesimal path element.

Why is the Voltage formula important in Physics?

Without voltage, there's no current — voltage is the driving force of every circuit.

What do students get wrong about Voltage?

Voltage exists between two points (it's a difference), not at a single point.

What should I learn before the Voltage formula?

Before studying the Voltage formula, you should understand: electric current.

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