9.2 Potential difference and power

Potential difference V is the energy transferred per coulomb when charge moves between two points: V=energy per charge.

Specify the component and direction of energy transfer. A source supplies energy; a resistor or motor transfers it to other stores.

A 6 V battery supplies 6 J to each coulomb passing through the external circuit ideally.

Potential difference is not current and is not “used up” as charge circulates; components have voltage drops or rises.

The potential difference across a component is V=W/Q, so W=VQ is the energy transferred when charge Q crosses it.

Use joules and coulombs, and identify whether W is supplied or dissipated. The sign depends on the chosen direction.

Moving 5 C through a 12 V motor transfers 60 J to mechanical and thermal stores.

A 12 V label is not 12 J total; it means 12 J per coulomb under the specified operating conditions.

For a component, power P=VI. Combining with V=IR gives P=I²R and P=V²/R, with the appropriate measured voltage and current.

Choose the form that uses known quantities and distinguish input power from useful output. These equations assume the component’s voltage-current relation at that operating point.

A 6 Ω resistor carrying 2 A dissipates P=I²R=24 W, also equal to VI when V=12 V.

Do not use P=V²/R for a non-ohmic device with a fixed resistance assumption unless its operating-point resistance is known.