Define electric current, voltage, and resistance, and use Ohm's law V = IR to relate them in a simple circuit (MA STE Introductory Physics, electric circuits).

What this topic is asking

This topic introduces the circuit quantities the Massachusetts Introductory Physics MCAS tests and the law that links them. You must define current (the flow of charge), voltage (the push that drives it), and resistance (what opposes it), and use Ohm's law $V = IR$ to relate them in a simple circuit. Ohm's law is on the reference sheet. The crosscutting idea is cause and effect: voltage causes a current to flow, and resistance limits how big that current is.

Current, voltage, and resistance

These three quantities describe every simple circuit, and the MCAS expects clear definitions:

• Current is charge in motion. In a metal wire it is a flow of electrons, though conventional current is drawn from the positive terminal of the battery to the negative. More charge flowing per second means a larger current.
• Voltage is the push. A battery sets up a potential difference that gives energy to the charges and makes them flow. Think of it as electrical "pressure."
• Resistance is the brake. Components such as resistors and bulbs oppose the flow, converting electrical energy into heat and light. A thin or long wire has more resistance than a thick or short one.

Ohm's law

The reference-sheet formula is

where $V$ is the voltage (V), $I$ is the current (A), and $R$ is the resistance (ohms). This single relationship answers most circuit calculations on the test:

• Given any two of the three, find the third by rearranging.
• At fixed voltage, current is inversely proportional to resistance: halving the resistance doubles the current.
• At fixed resistance, current is directly proportional to voltage: doubling the battery voltage doubles the current.

A graph of voltage against current for a fixed resistor is a straight line through the origin, and its steepness reflects the resistance.

Worked example

Reference-sheet note

The reference sheet prints Ohm's law as $V = IR$, with $V$ in volts, $I$ in amperes, and $R$ in ohms. What you recall is the meaning of each quantity (current is flowing charge, voltage is the driving push, resistance is the opposition), the rearrangements $I = V/R$ and $R = V/I$, and the inverse relationship between current and resistance at fixed voltage.

Try this

Q1. A current of $2.0$ A flows through a $5.0$ ohm resistor. Calculate the voltage across it. [2]

• Cue. $V = IR = (2.0)(5.0) = 10$ V.

Q2. A $9.0$ V battery drives a current of $3.0$ A through a component. Calculate its resistance. [2]

• Cue. $R = \dfrac{V}{I} = \dfrac{9.0}{3.0} = 3.0$ ohms.