AP Physics C: E&M · Topic 11.2

Topic 11.2: Simple Circuits

Unit 11: Electric Circuits15-25% of the multiple-choice section

A circuit is composed of electrical loops built from wires, batteries, resistors, bulbs, capacitors, inductors, switches and meters. Closed means charge can flow, open means it cannot, short means it can flow with no change in potential difference. One element can sit in more than one loop.

AP Physics: Unit 11 (topics 11.2 Simple Circuits). Topic 11.2 of the current AP Physics C: Electricity and Magnetism course and exam description, in Unit 11 Electric Circuits (15 to 25% of the multiple-choice section, about 12 to 24 class periods). One learning objective, 11.2.A, describe the behavior of a circuit, carrying nine essential knowledge statements: 11.2.A.1, 11.2.A.2 with sub-statements i to iii, 11.2.A.3, and 11.2.A.4 with sub-statements i and ii. The topic contains no equation, the only Unit 11 topic with none. Its boundary statement reads in full: unless otherwise specified, all circuit schematic diagrams will be drawn using conventional current. Statement 11.2.A.4.ii prints eight schematic symbols, battery, bulb, switch, capacitor, resistor, ammeter, voltmeter and inductor, and states that variable elements are indicated by a diagonal strikethrough arrow across the standard symbol for that element. The AP Physics 2 version of this topic is the same nine statements with the same boundary statement, but its element list omits inductors and it prints seven symbols rather than eight. Suggested skills 1.A, 2.C, 3.B and 3.C. The course description's Instructional Approaches section works a case study on a Unit 11 circuit of two identical lightbulbs and a switch connected to a battery, with one multiple-choice question written against each of skills 2.A, 2.B, 2.C, 2.D, 3.B and 3.C off that single stimulus.

What Topic 11.2 requires

Topic 11.2 of AP Physics C: Electricity and Magnetism Unit 11 has one learning objective and nine essential-knowledge statements, and it prints one boundary statement.

11.2.A, describe the behavior of a circuit.

11.2.A.1 A circuit is composed of electrical loops, which can include wires, batteries, resistors, lightbulbs, capacitors, inductors, 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.

Boundary statement, quoted whole: "Unless otherwise specified, all circuit schematic diagrams will be drawn using conventional current."

The suggested skills are 1.A, create diagrams, tables, charts, or schematics to represent physical situations; 2.C, compare physical quantities between two or more scenarios or at different times and locations in a single scenario; 3.B, apply an appropriate law, definition, theoretical relationship, or model to make a claim; and 3.C, justify or support a claim using evidence from experimental data, physical representations, or physical principles or laws.

There is no equation anywhere in Topic 11.2. It is the only topic in Unit 11 with none, and that tells you what the topic is: vocabulary and representation, tested by asking you to reason about a picture.

Be honest about the overlap: this topic is almost identical to AP Physics 2

Most Physics C topics differ from their algebra-based twin because calculus changes something. This one does not, and pretending otherwise would waste your time. All nine statements appear in the AP Physics 2 framework in the same order, with wording that is identical apart from one item in one list, and both courses carry the identical boundary statement about conventional current. There is no derivative and no integral anywhere in Topic 11.2 in either course.

Two real differences exist, both to do with the inductor, and they are small but worth knowing.

The C element list adds inductors. Statement 11.2.A.1 in AP Physics C reads "wires, batteries, resistors, lightbulbs, capacitors, inductors, switches, ammeters, and voltmeters". The AP Physics 2 version of the same statement lists the same elements minus inductors. That is not a wording quirk; it is Unit 13 reaching back into Unit 11. A C circuit can legitimately contain an inductor from the moment you meet schematics.

The C symbol set has eight symbols; the Physics 2 set has seven. Statement 11.2.A.4.ii prints the symbols themselves. In AP Physics C the printed set is battery, bulb, switch, capacitor, resistor, ammeter, voltmeter and inductor. AP Physics 2 prints the first seven and stops.

The suggested skills do not differ at all. Both courses list 1.A, 2.C, 3.B and 3.C for this topic. That is unusual across Unit 11: on Topic 11.4 the two courses share no suggested skill at all, and on Topics 11.5 and 11.7 they differ by one or more. Here they match exactly.

So: if you want a fuller treatment of the vocabulary itself, the AP Physics 2 Topic 11.2 page covers exactly this ground and is written for the algebra-based exam. This page spends its remaining space on the two things that are different for a C student: the inductor, and what the C free-response section actually does with a schematic.

Loops, not parts: the definition that gets tested

Statement 11.2.A.1 does not say a circuit is a collection of components. It says a circuit is composed of electrical loops, and 11.2.A.3 adds that a single circuit element may be part of multiple electrical loops. Together those two lines are the whole of circuit analysis in miniature.

Why the loop framing matters:

[Kirchhoff's loop rule](/ap-physics-c-electricity-magnetism/unit-11-electric-circuits/11-6-kirchhoffs-loop-rule) is written per loop. Statement 11.6.A.2.i says the sum of potential differences across all circuit elements in a single closed loop must equal zero. Before you can apply it you have to have identified the loops, and 11.2.A.3 is warning you that a resistor sitting in two loops appears in two equations.
The number of independent loops sets the number of equations. A network with two loops and one junction gives you two independent loop equations and one junction equation, which is enough for three unknown currents.
A loop that is broken is not a loop. An open switch does not remove an element from the diagram; it removes a path, and with it every loop that used that path.

Statement 11.2.A.4.i is the same idea from the other end: the properties of an electric circuit are dependent on the physical arrangement of its constituent elements. Two bulbs and a battery is not a circuit description. Two bulbs in series with a battery, and two bulbs in parallel across a battery, are two different circuits built from identical parts, and they behave nothing alike.

That statement is also the licence for the whole family of questions where you are handed the same components twice and asked what changed. Skill 2.C, comparing quantities between two scenarios, is listed on this topic precisely for that.

Closed, open and short, and why the short is the awkward one

Statement 11.2.A.2 defines a closed electrical loop as a closed path through which charges may flow, and its three sub-statements name the three states.

State	CED wording (11.2.A.2.i to iii)	What it does to a branch
Closed	charges would be able to flow	normal operation
Open	charges would not be able to flow	zero current in that branch
Short	charges would be able to flow with no change in potential difference	zero potential difference across it

Closed and open are intuitive. The short is the one that trips people, because the CED defines it by potential difference, not by current. A short circuit is a path with no change in potential difference across it, which by $I = \Delta V / R$ means it must have effectively zero resistance, and which means any element bridged by it also has zero potential difference across it and therefore carries no current.

That single chain of reasoning answers a large fraction of switch questions:

Close a switch that provides a zero-resistance path across an element.
The element now has zero potential difference across it.
By Ohm's law the element carries zero current, so a bulb goes dark.
Everything else in the circuit sees a lower total resistance, so the total current rises.

The CED works exactly this circuit in its Instructional Approaches section. A battery is in series with Bulb 1; Bulb 2 is in parallel with a switch. With the switch open the two bulbs are in series and, in the CED's own question, they have equal brightness. Its skill 2.A question asks for the power delivered to Bulb 1 with the switch open, and the credited expression is $P = \mathcal{E}^2 / (4R)$ , which is what you get from $I = \mathcal{E}/(2R)$ and $P = I^2 R$ . Its skill 2.C question then asks what happens when the switch is closed, and the credited answer is that Bulb 1 gets brighter while Bulb 2 goes out.

One caution the CED does not spell out but the reference information does. "Short" describes a path, not a fault. A closed ideal switch, an ideal ammeter and an ideal wire all short whatever they bridge, and the exam's standing convention is that strings, springs, batteries, wires and meters are ideal unless a question says otherwise.

The eight schematic symbols, and the inductor

Statement 11.2.A.4.ii prints the symbol set and one rule about it. The printed symbols in the AP Physics C: Electricity and Magnetism framework are:

Battery, drawn as alternating long and short parallel lines. The long line is the positive terminal.
Bulb, a circle containing a filament loop.
Switch, a hinged line that either touches the second contact or does not.
Capacitor, two equal parallel lines, distinguishable from the battery precisely because they are equal.
Resistor, a zigzag.
Ammeter, a circled A.
Voltmeter, a circled V.
Inductor, a coil of loops. This is the one AP Physics 2 does not print.

The rule is the second sentence: variable elements are indicated by a diagonal strikethrough arrow across the standard symbol for that element. So a resistor zigzag with a diagonal arrow through it is a variable resistor, and the same arrow across a capacitor makes a variable capacitor. That notation is how a question tells you which quantity it is going to change, and skill 2.D, functional dependence, is what it wants you to do about it.

The battery and capacitor symbols are the pair worth a second look, because they are two parallel lines either way. Unequal lines mean a battery, equal lines mean a capacitor. In a hand-drawn free-response answer, draw them unmistakably: a schematic is the representation you are graded on under skill 1.A, and an ambiguous symbol earns nothing.

The inductor is not decoration on this list. Once it appears, three Unit 13 behaviours become available in a Unit 11 style question: an inductor opposes a change in current, it behaves like a wire with zero resistance long after a switch closes, and a series LR circuit has time constant $\tau = L / R_{\text{eq}}$ , which is printed on the C: E&M sheet a few lines below $\tau = R_{\text{eq}} C_{\text{eq}}$ . Topic 13.5 is where that gets developed.

The conventional-current boundary statement, and what it does not cover

The boundary statement is short and worth memorising verbatim: "Unless otherwise specified, all circuit schematic diagrams will be drawn using conventional current."

Read both halves. The second half sets the default: every arrow on every schematic points the way positive charge would move, which is out of the long terminal of the battery and back into the short one. The first half, "unless otherwise specified", is the exception clause, and it means a question is allowed to switch the convention off by saying so. If a stem talks about electron flow, it has done that on purpose and the arrows reverse.

The exam's reference information repeats the convention as one of seven standing rules: the direction of current is the direction in which positive charges would drift. Statement 11.1.A.4.ii from Topic 11.1 is candid that this is a bookkeeping choice: in common circuits the current is actually due to the movement of electrons, which are negative charge carriers moving the other way.

Nothing physical depends on the choice, and that is the point. Power dissipated, brightness, potential differences and meter readings all come out the same either way. What does depend on it is the sign of your loop-rule terms, so declare a direction once at the top of a solution and hold it.

Two things the boundary statement deliberately does not do:

It does not say the arrow you draw has to be the true direction. In a multi-loop network you are allowed to guess, and a negative answer tells you the current runs the other way. That is standard practice and costs no marks.
It does not limit which elements can appear. Unlike the boundary statements on Topics 11.4 and 11.5, this one restricts a drawing convention rather than the physics you are asked to analyze.

How Topic 11.2 is tested

Topic 11.2 supplies no equation, so it is never the whole of a question. It arrives in three recognisable ways.

As the skill 3.B claim about arrangement. The CED's own case-study question for skill 3.B, built on that two-bulb circuit, is: which of the following claims about the arrangement of the circuit is correct? The credited answer is that the two bulbs are in series with each other. Series and parallel are defined in Topic 11.5 at 11.5.A.1.i and 11.5.A.1.ii, but the ability to read them off a drawing is Topic 11.2.

As the first mark of a free-response question. Skill 1.A, creating a schematic, is a Science Practice 1 skill, and the exam weighting table lists all of Science Practice 1 as N/A on the multiple-choice section and 20 to 35% of the free-response section. A drawing that is asked for is a drawing that is scored.

As a switch or a redrawing. Skills 2.C and 3.C are both listed here, and the pattern is a before-and-after: open the switch, close the switch, move a wire, and justify what changed using a physical principle rather than a computed number.

A practical habit that turns most of these into short questions: redraw the circuit with the switch in the stated position before doing anything else. Erase the branch an open switch blocks, and collapse to a single node every point joined by ideal wire and closed switches. What looks like a compound network usually reduces to something obvious once nodes that are electrically the same point are drawn as the same point.

From here, Topic 11.3 gives the elements electrical characteristics, and the series and parallel guide owns the reduction routine itself. The ammeter against voltmeter comparison covers the two meter symbols in detail.

A switch that shorts a bulb: reading the CED's own circuit

A battery of emf $\mathcal{E}$ and negligible internal resistance is in series with Bulb 1, of resistance $R$ . Bulb 2, also of resistance $R$ , is in parallel with a switch. Both bulbs are ohmic. Find, symbolically, (a) the current in Bulb 1 and the power delivered to it with the switch open, (b) the same two quantities with the switch closed, and (c) the ratio of Bulb 1's brightness in the two cases. Then state what happens to Bulb 2.

Declare the convention: conventional current, per the Topic 11.2 boundary statement, running out of the long battery terminal. Hold it to the end.
(a) Switch open. The switch branch is an open circuit by 11.2.A.2.ii, so no charge flows through it and the only loop runs battery, Bulb 1, Bulb 2. The two bulbs are in series, so $R_{\text{eq}} = 2R$ and Ohm's law in the printed form gives $I_o = \dfrac{\mathcal{E}}{2R}$ .
Power to Bulb 1 from $P = I^2 R$ , the derived form of 11.4.A.1: $P_o = \left(\dfrac{\mathcal{E}}{2R}\right)^2 R = \dfrac{\mathcal{E}^2}{4R}$ . This matches the credited expression in the CED's own skill 2.A case-study question for this circuit.
(b) Switch closed. The closed ideal switch is a path with zero resistance across Bulb 2, so by 11.2.A.2.iii Bulb 2 now has no change in potential difference across it. Zero potential difference across an ohmic element means zero current in it: Bulb 2 goes out.
The battery now sees Bulb 1 alone: $I_c = \dfrac{\mathcal{E}}{R}$ , and $P_c = I_c^2 R = \dfrac{\mathcal{E}^2}{R}$ .
(c) $\dfrac{P_c}{P_o} = \dfrac{\mathcal{E}^2 / R}{\mathcal{E}^2 / (4R)} = 4$ . Bulb 1 dissipates four times the power, so by 11.4.A.2, which says brightness increases with power, it gets brighter. The current only doubles, but power goes as the square of current at fixed resistance.
Numerical check with the CED's own values, $R = 2.0\ \Omega$ and $\mathcal{E} = 9.0$ V, switch open: $P_o = \dfrac{(9.0)^2}{4(2.0)} = \dfrac{81}{8.0} = 10.125$ W, which is most nearly 10 W. That is the credited answer to its skill 2.B question.

(a) $I_o = \mathcal{E}/(2R)$ and $P_o = \mathcal{E}^2/(4R)$ , which is 10 W for $R = 2.0\ \Omega$ and $\mathcal{E} = 9.0$ V. (b) $I_c = \mathcal{E}/R$ and $P_c = \mathcal{E}^2/R$ . (c) Bulb 1's power rises by a factor of 4, so it gets brighter, while Bulb 2 goes out because the closed switch shorts it.

Counting loops, and finding the ones that share an element

A battery is connected to a node A. From A, two parallel branches run to node B: branch 1 contains resistor $R_1$ , branch 2 contains resistor $R_2$ . From B a single wire containing $R_3$ returns to the battery. (a) How many closed loops does this circuit contain? (b) Which elements belong to more than one loop? (c) How many independent equations do you need to find all three branch currents, and where do they come from?

(a) Trace every closed path. Loop I: battery, $R_1$ , $R_3$ . Loop II: battery, $R_2$ , $R_3$ . Loop III: $R_1$ from A to B, then back through $R_2$ from B to A, which never touches the battery. Three closed loops. Students routinely find the first two and miss the third, because it contains no source.
Statement 11.2.A.2 defines a closed electrical loop as a closed path through which charges may flow, and it says nothing about needing a battery in it. Loop III qualifies.
(b) By 11.2.A.3 a single element may be part of multiple loops. Here $R_1$ is in loops I and III, $R_2$ is in loops II and III, $R_3$ is in loops I and II, and the battery is in loops I and II. Every element in this circuit sits in exactly two loops.
(c) Three unknown currents need three independent equations. Only two of the three loop equations are independent: loop III is the difference of loops I and II, so it adds nothing. The third equation comes from the junction rule at node A, $I_{\text{battery}} = I_1 + I_2$ , which is 11.7.A.2.
General rule to carry forward: the number of independent loop equations is the number of loops that enclose no other loop, and the junction rule supplies the rest. Here that is 2 plus 1.
Sanity check on the topology: $R_1$ and $R_2$ share both of their end nodes, A and B, which is the 11.5.A.1.ii definition of a parallel connection, and $R_3$ carries the whole battery current, which is the 11.5.A.1.i definition of series. So this network is $R_1$ parallel $R_2$ , all in series with $R_3$ , and the three-equation route must agree with reducing it that way.

(a) Three closed loops, including one that contains no battery. (b) All four elements sit in exactly two loops each. (c) Three equations: two independent loop equations plus one junction equation at node A. The network is $R_1$ in parallel with $R_2$ , that combination in series with $R_3$ .

Frequently asked questions

What is a short circuit in AP Physics?

The AP Physics C course description defines it by potential difference rather than by current. Essential knowledge 11.2.A.2.iii says a short circuit is one in which charges would be able to flow with no change in potential difference. Because Ohm's law relates current, resistance and potential difference across an element, a path with no change in potential difference across it must have effectively zero resistance, and any element bridged by that path also has zero potential difference across it and therefore carries no current. That is why closing a switch across a bulb makes the bulb go dark while the total current in the circuit rises.

What circuit symbols does the AP Physics C E&M course description print?

Eight, at essential knowledge 11.2.A.4.ii: battery, bulb, switch, capacitor, resistor, ammeter, voltmeter and inductor. The AP Physics 2 framework prints the same set without the inductor. The same statement adds one rule for reading them: variable elements are indicated by a diagonal strikethrough arrow across the standard symbol for that element, so a resistor zigzag with an arrow through it is a variable resistor. The battery and capacitor symbols are the pair most often confused, since both are parallel lines. Unequal line lengths mean a battery, and equal lines mean a capacitor.

Does the AP Physics C exam use conventional current or electron flow?

Conventional current, by default. The Topic 11.2 boundary statement reads in full: unless otherwise specified, all circuit schematic diagrams will be drawn using conventional current. The exam's reference information repeats it as a standing convention, that the direction of current is the direction in which positive charges would drift. The phrase unless otherwise specified is the exception clause and it matters: a question is allowed to switch the convention off by saying so, and a stem that talks about electron flow has done exactly that. Essential knowledge 11.1.A.4.ii is candid that in common circuits the current is actually due to the movement of electrons.

Can one circuit element be part of more than one loop?

Yes, and the AP Physics C course description says so at essential knowledge 11.2.A.3: a single circuit element may be part of multiple electrical loops. This is the reason Kirchhoff's loop rule produces a system of equations rather than a single one, since a resistor sitting in two loops appears in two of them. A related counting point is that not every closed loop needs to contain a battery. In a network of two parallel resistors fed by a source, the path that runs out through one resistor and back through the other is a closed loop by the essential knowledge 11.2.A.2 definition, even though it contains no source.

Is AP Physics C Topic 11.2 different from AP Physics 2 Topic 11.2?

Barely. The nine essential knowledge statements appear in both frameworks in the same order, both courses print the identical boundary statement about conventional current, both list the same four suggested skills, and neither topic contains a single equation. Two small differences exist, and both concern the inductor. The AP Physics C element list at essential knowledge 11.2.A.1 includes inductors and the AP Physics 2 list does not, and the AP Physics C symbol set prints eight symbols including the inductor where AP Physics 2 prints seven. If your course is the algebra-based one, the AP Physics 2 page covers this topic completely.

How do you tell whether elements are in series or parallel from a schematic?

Use the definitions in Topic 11.5 rather than the shape of the drawing. Essential knowledge 11.5.A.1.i says a series connection is one in which any charge passing through one element must proceed through all elements in that connection and has no other path available, so elements in series carry the same current. Essential knowledge 11.5.A.1.ii says a parallel connection is one in which charges may pass through one of two or more paths, and across each path the potential difference is the same. The practical test is to check whether two elements share both of their end nodes, which makes them parallel, or whether one element carries every charge that passed through the other, which makes them series.