Voltage and potential energy

YOU WILL BE ABLE TO

Define voltage as energy per unit charge, v = dw/dq.
Explain why voltage is always measured between two points.
Interpret polarity marks (+/−) and use a reference node (ground).
Distinguish a voltage rise from a voltage drop.

Current tells you charge is moving; voltage tells you why. Moving charge through a circuit element either costs energy or releases it, and voltage is the exchange rate: the energy transferred per coulomb of charge moved between two points.

v = \frac{dw}{dq}

voltage, volts

One volt (V) is one joule per coulomb. A 9 V battery does 9 joules of work on every coulomb it pushes from its − terminal to its + terminal. This is exactly analogous to gravitational potential energy: lifting a mass to a height stores energy; letting it fall releases it. Voltage is electrical height.

On a schematic, a voltage is labelled with + and − marks. The statement v_AB = 5 V means point A is 5 V above point B. Equivalently, v_BA = −5 V — a negative voltage is not exotic, it just means the polarity is opposite to the labels. Getting comfortable with "negative just means opposite to the arrow/label" now will save you endless grief in nodal analysis (CA-3).

Travelling through an element from − to + is a voltage rise (energy gained by the charge — what happens inside a source). Travelling from + to − is a voltage drop (energy released — what happens in a resistor or an LED). A single element is a rise or a drop depending on which way you traverse it; the physics doesn't change, only your bookkeeping direction.

WORKED EXAMPLE

Energy from a battery

A 9 V battery pushes 5 C of charge through a circuit.
w = v·q (for constant voltage).
w = 9 V × 5 C = 45 J.

45 J delivered by the battery

WORKED EXAMPLE

Reading polarity

An element is labelled + on top, − on bottom, with v = −3 V.
The negative value means the top is actually 3 V below the bottom.
Equivalently: flip the labels and write v = +3 V. Same physical situation.

The bottom terminal is 3 V above the top terminal.

PRACTICE

Moving 20 mC of charge through an element releases 0.1 J. What is the voltage across it?

A phone charger operates at 5 V. How much energy does it give each coulomb, and how much energy is delivered if 3600 C flows during a charge?

If v_AB = 12 V, what is v_BA, and which point is at the higher potential?

Node A is at 3.3 V and node B is at 1.8 V, both measured from ground. What is v_AB? (These are the two logic-supply voltages you'll meet constantly in microelectronics.)