Define current as rate of flow of charge, $I = q/t$, state Ohm's law $R = V/I$, and apply the electrical power equations to calculate power and energy in a resistor.

What this topic is asking

This dot point covers the core of circuit electricity: current as the flow of charge, Ohm's law relating voltage, current and resistance, and the power and energy delivered to a component. The Physical Setting/Physics course asks you to define current as $I = \dfrac{q}{t}$, to apply Ohm's law $R = \dfrac{V}{I}$, and to use the electrical power equations. These are among the most frequently tested Regents calculations, in both Part B and Part C.

Electric current

Current is driven by a potential difference: a battery maintains a voltage that pushes charge around the circuit. The amount of current depends on both the voltage applied and the resistance of the circuit. Counting the charge that passes in a given time, or finding the time for a given charge, uses $I = \dfrac{q}{t}$ directly.

Ohm's law

Ohm's law says that, for a given resistance, the current is proportional to the voltage: doubling the voltage doubles the current. Resistance measures how strongly a component opposes current; a larger resistance gives a smaller current for the same voltage. For an "ohmic" conductor at constant temperature, $R$ is constant, so a graph of voltage against current is a straight line through the origin whose slope is the resistance, a relationship the Regents sometimes tests with a data plot.

Electrical power and energy

The three forms of the power equation are equivalent; choose the one matching the quantities you have. $P = VI$ uses voltage and current directly; $P = I^2 R$ is handy when current and resistance are known; $P = \dfrac{V^2}{R}$ when voltage and resistance are known. The energy $W = Pt$ is what an appliance consumes over time and what an electricity bill charges for.

Reference Tables note

The Electricity section of the Reference Tables prints $I = \dfrac{q}{t}$, Ohm's law $R = \dfrac{V}{I}$, the three power equations $P = VI$, $P = I^2 R$ and $P = \dfrac{V^2}{R}$, and the energy relation $W = Pt$. You supply the rearrangements (such as $V = IR$) and the choice of which power form fits the given data. The series and parallel rules for combining resistors are treated in series and parallel circuits.

Try this

Q1. A current of $2.0$ A flows for $30.$ s. Calculate the charge that passes. [2 points]

• Cue. From $I = \dfrac{q}{t}$, $q = It = (2.0)(30.) = 60.$ C.

Q2. A $12$ V source drives $3.0$ A through a resistor. Calculate the power dissipated. [2 points]

• Cue. $P = VI = (12)(3.0) = 36$ W.