Topic 11.2: Simple Circuits

What Topic 11.2 requires

Topic 11.2 carries one learning objective, 11.2.A: describe the behavior of a circuit. Four essential knowledge statements sit under it, and two of them add sub-statements.

• 11.2.A.1 A circuit is composed of electrical loops, which may include circuit elements such as wires, batteries, resistors, lightbulbs, capacitors, switches, ammeters, and voltmeters.
• 11.2.A.2 A closed electrical loop is a closed path through which charges may flow.
• 11.2.A.2.i A closed circuit is one in which charges would be able to flow.
• 11.2.A.2.ii An open circuit is one in which charges would not be able to flow.
• 11.2.A.2.iii A short circuit is one in which charges would be able to flow with no change in potential difference.
• 11.2.A.3 A single circuit element may be part of multiple electrical loops.
• 11.2.A.4 Circuit schematics are representations used to describe and analyze electric circuits.
• 11.2.A.4.i The properties of an electric circuit are dependent on the physical arrangement of its constituent elements.
• 11.2.A.4.ii Circuit elements have common symbols that are used to create schematic diagrams. Variable elements are indicated by a diagonal strikethrough arrow across the standard symbol for that element.

The topic's boundary statement is a single sentence: unless otherwise specified, all circuit schematic diagrams will be drawn using conventional current.

That is why a bare arrow on a wire in an AP Physics 2 diagram needs no caption. It is conventional current, the direction positive charge would move, which is Topic 11.1's essential knowledge 11.1.A.2.i. The exception clause carries as much weight as the rule: a question is free to specify otherwise, and then the arrow means whatever the question says it means.

The CED lists four suggested skills here, and they are the same four it lists for Topic 11.1, where the full wording is set out: 1.A, create diagrams, tables, charts, or schematics; 2.C, compare physical quantities between scenarios or at different times; 3.B, apply a law, definition, theoretical relationship, or model to make a claim; and 3.C, justify or support a claim using evidence. Unit 11 is weighted at 15 to 18 percent of the multiple-choice section, with roughly 12 to 20 suggested class periods.

Now notice something about that list: Topic 11.2 prints no equation at all. Other topics in this unit print a relevant equation beside an essential knowledge statement; this one does not. The assessable content is definitions, loop structure and reading a representation.

A circuit is a set of loops, not a list of parts (11.2.A.1 and 11.2.A.3)

The CED's definition leads with the loops and treats the hardware as filling: a circuit is composed of electrical loops, which may include circuit elements such as wires, batteries, resistors, lightbulbs, capacitors, switches, ammeters, and voltmeters. Note the phrase "may include". The elements are the contents; the loop is the thing.

That ordering pays off immediately, because 11.2.A.3 says a single circuit element may be part of multiple electrical loops. A battery feeding two branches belongs to both, and a resistor in the trunk of a circuit that splits downstream belongs to every loop running through that trunk. Elements are not privately owned, so a change in one loop can reach another through a shared element.

To count loops on a diagram, trace with a finger. Start anywhere, move only along wires and through elements, and see whether you can return to your starting point without reusing a wire. Each distinct route that closes is a loop. One battery and one resistor gives exactly one. Split the path into two branches and you can trace three closed routes: one through each branch, and one that runs down one branch and back up the other without touching the source at all. That third route is a genuine loop, and Kirchhoff's loop rule applies to it just as it does to the other two.

Two consequences for reading a diagram. Count paths before you count parts, because how many routes charge can take decides whether elements share a current or share a potential difference. And a break matters only where it breaks a loop: opening a switch in a single-loop circuit stops everything, while opening one in a branch stops that branch and leaves any loop that avoids it intact. That is the physics behind the unit's essential question about why several bulbs on a string of lights go out when one bulb is unplugged.

Closed, open and short: the three states the CED names (11.2.A.2)

Essential knowledge 11.2.A.2 defines the loop itself: a closed electrical loop is a closed path through which charges may flow. Three sub-statements then name the three states you are expected to identify.

Two features of that wording are worth pausing on.

First, all three sub-statements are written in the conditional: charges would be able to flow, or would not. They describe what the path permits, not whether anything is flowing right now. A closed loop with no source in it is still a closed circuit. Getting this right keeps you from calling a circuit "open" merely because the current happens to be zero.

Second, the CED defines a short by its potential difference, not by heat, sparks or a large current. In an exam circuit the wires are ideal, so any ideal wire connected across an element shorts that element: the two ends are joined by a path with zero potential difference between them, so the element has zero potential difference across it and therefore no current through it. The third worked example below walks that through with numbers.

The schematic is a representation, and it is the one you are graded on (11.2.A.4)

Essential knowledge 11.2.A.4 says circuit schematics are representations used to describe and analyze electric circuits, and 11.2.A.4.ii supplies the symbol set. The CED prints seven.

Two details of that set repay a second look. The switch is drawn in the open position, so the symbol tells you the state as well as the element. And the capacitor's two lines are the same length while the battery's alternate long and short, which is the difference to check when either is drawn small.

11.2.A.4.ii also gives the one modifier the CED defines: variable elements are indicated by a diagonal strikethrough arrow across the standard symbol for that element. A resistor zigzag with a diagonal arrow through it is a variable resistor. That arrow is not a current arrow and does not point anywhere in the circuit.

The deeper point in 11.2.A.4 is that a schematic is a topological drawing. It records which elements are joined to which, not how long the wires are or where anything sits on the page. Two diagrams that look nothing alike are the same circuit when the connections match, and two that look almost identical are different circuits when one wire moves. Wire length carries no meaning: Topic 11.5's essential knowledge 11.5.B.1 says ideal wires have negligible resistance.

Suggested skill 1.A is listed first for this topic, and turning a verbal description into a correct schematic is its most direct form. Practise it in both directions.

Reading a single-loop schematic

The smallest circuit that does anything is an ideal battery, a resistor and the wires joining them: one loop, one current, and every element carries that same current because there is nowhere else for charge to go. Read a diagram like this in a fixed order.

1. Find the source and its terminals. By the usual drafting convention the longer line of the battery symbol is the higher-potential terminal. The CED prints the symbol without a plus or minus label, so identify the terminals from the labels or the current arrow a question supplies rather than from memory.
2. Fix the direction of the current. The boundary statement settles it: unless otherwise specified, the diagram uses conventional current. It runs out of the higher-potential terminal, around the external part of the loop, and back into the other terminal.
3. Look for breaks and shortcuts. One open switch anywhere in a single-loop circuit makes the whole thing open and the current zero (11.2.A.2.ii). Any element with an ideal wire across it is shorted, so it carries no current and has no potential difference across it (11.2.A.2.iii).
4. Walk the loop and track the potential. It rises across the battery from the lower-potential terminal to the higher, drops across the resistor in the direction of the conventional current, and does not change along an ideal wire.

That last step is the informal version of a rule you meet formally in Topic 11.6. The reason the rises and drops must cancel over a complete loop is conservation of energy, which is what the unit opener means when it says Unit 11 revisits the behavior of charged particles to deepen students' understanding of the law of conservation of energy and its application to electric circuits.

To turn a single-loop schematic into a number for the current you need Ohm's law, and Ohm's law is Topic 11.3. The AP Physics 2 sheet prints it as $I = \frac{\Delta V}{R}$, with the delta, because the numerator is a potential difference. The worked examples below use it purely as a tool so a schematic can produce a number; resistance, resistivity and what makes an element ohmic belong to 11.3, and the step-by-step routine lives in the Ohm's law guide and the Ohm's law calculator.

The arrangement is the circuit (11.2.A.4.i)

Essential knowledge 11.2.A.4.i is one line long: the properties of an electric circuit are dependent on the physical arrangement of its constituent elements.

It is the whole reason schematics exist. A parts list is not a circuit. One battery and two resistors can be wired as a single loop or with each resistor straight across the battery's terminals, and the two circuits differ in the current the battery delivers, the potential difference across each resistor, and what happens when one is removed. The second worked example below puts a factor of four between the two battery currents.

Two habits follow from taking 11.2.A.4.i seriously.

• Decide what is joined to what before computing anything. Reading the arrangement is a separate step from calculating, and doing it second is where avoidable errors enter.
• When a question changes the circuit, redraw it. A bulb removed, a switch thrown, a wire added: each is a new schematic. The unit's Developing Understanding note is explicit that students must be able to articulate the impact of a light bulb being removed from a circuit, which is a question about arrangement rather than arithmetic.

One of the unit's essential questions lands here: "Why do several bulbs on a string of lights go out when one bulb is unplugged?" is 11.2.A.4.i and 11.2.A.2.ii together, since unplugging a bulb opens a loop and whether other bulbs go dark depends on whether they sit in it.

Systematic reduction of series and parallel groups is Topic 11.5's content, and the routine for it is in the series vs parallel guide. Topic 11.2 sits one level above: recognise that the arrangement is itself a property of the circuit, and read it correctly off the diagram before any formula comes out.

What "ideal" means here, and where the CED spells it out

Every element in a Topic 11.2 problem is ideal unless the question says otherwise, and that is printed rather than assumed. The AP Physics 2 Table of Information carries nine conventions used on the exam unless otherwise stated, and three of them govern circuits:

• "Strings, springs, batteries, wires, and meters are ideal."
• "Resistors and lightbulbs are ohmic."
• "Capacitors are air-filled ($\kappa = 1.0$)."

The CED spells out what ideal means in Topic 11.5 rather than here. Essential knowledge 11.5.B.1 states that ideal batteries have negligible internal resistance and ideal wires have negligible resistance; 11.5.C.1.ii, that ideal ammeters have zero resistance so that they do not affect the current in the element they are in series with; and 11.5.C.2.ii, that ideal voltmeters have an infinite resistance so that no charge flows through them. The Topic 11.5 boundary statement then restates the default in the CED's own voice: AP Physics 2 only expects students to qualitatively discuss how a nonideal ammeter or voltmeter will affect the results of measurements; unless otherwise stated, all batteries, wires, and meters are assumed to be ideal; and circuits with batteries of different potential differences connected in parallel will not be assessed.

For reading a Topic 11.2 diagram, three consequences do the work.

• An ideal battery holds the same potential difference across its terminals whatever current the circuit draws, having no internal resistance for the current to drop potential across.
• An ideal wire has no potential difference across it however much current it carries. That is why an ideal wire laid across an element produces a short circuit in the sense of 11.2.A.2.iii, and why connecting-wire resistance never enters the arithmetic.
• An ideal meter does not disturb what it measures.

None of these are approximations you invent to make a problem tractable. They are stated conventions, so you can cite them in a justification instead of apologising for them.

How Topic 11.2 is tested, and where it leads

The four suggested skills describe four things a question can ask.

• 1.A Draw the schematic for a described circuit, with correct symbols and correct connections.
• 2.C Compare two scenarios: before and after a switch is thrown, or two arrangements of the same components side by side.
• 3.B Apply the definitions in 11.2.A.2: classify the circuit, then claim what the current does.
• 3.C Justify that claim, with the schematic itself as the physical representation you cite.

Because Topic 11.2 has no equation, its questions tend to be verbal, and the unit's Preparing for the AP Exam note warns that students should know the differences in meaning between "current", "potential difference", "resistance", "resistivity", and "capacitance". Saying "no voltage flows", or "there is no current because the circuit is shorted", is the kind of wording that loses justification points even when the underlying idea is right.

Where the topic leads:

• Topic 11.3 supplies the relationship between current, potential difference and resistance that turns a schematic into numbers, and Topic 11.4 adds the rate at which an element transfers energy.
• Topic 11.5 generalises the single loop to compound circuits, and defines ideal batteries, wires and meters.
• Topic 11.6 and Topic 11.7 turn loop tracing and junction counting into rules.
• Topic 11.8 puts a capacitor from Topic 10.6 into the loop, at which point the current stops being steady.