Simple Circuits
Translate physical connections into schematics, nodes, branches, and actual loops.
AP Physics 2 Topic 11.2 · College Board CED printed p. 62, 63 / PDF p. 69, 70 · See this topic in the course outline
A circuit schematic is a map of connections. Follow the path and identify nodes before deciding which components affect one another.
For a supporting original reading, see Introduction to Circuits. Practice node connectivity, switches and common symbols. Check that any short-circuit idealization retains a finite current-limiting resistance.
Before you start
Closed paths, open paths, and shorts
A circuit is made of electrical loops and elements: wires connect; batteries maintain voltage; resistors oppose current and transfer energy to heat; bulbs convert energy into heat and light; capacitors separate charge; switches change connectivity; ammeters measure current; voltmeters compare potential at two points.
A closed loop is a complete path along which charge can flow. An open switch interrupts a conducting path, so a simple series loop with that switch has no steady current. The source can still have a voltage across its terminals or across the open gap. In a branching circuit an open switch can stop one branch without stopping another.
A short is a conducting connection with negligible potential change along it. An ideal wire forces its two endpoints to the same potential. To use that rule, check the rest of the network: a load supplied through a finite series feed resistance can be bypassed by an ideal wire. The load voltage and current become zero, while the feed resistance limits the source current and takes the voltage drop.
A finite-resistance shunt directly across an ideal fixed-voltage battery is a different case. The battery continues fixing the load voltage, so the load current stays unchanged; the shunt adds a large extra current. An ideal zero-resistance wire directly across that ideal battery imposes both zero volts and the nonzero source emf on the same nodes. Those conditions are inconsistent, so there is no finite steady current to calculate. Real wire and internal resistance limit an actual battery short, which can cause substantial heating. Never demonstrate a direct battery short in class.
Symbols and nodes say more than page layout
Common schematic symbols are shown below. Battery long and short lines denote positive and negative terminals. A capacitor uses two equal plate lines; a resistor is a zigzag (a rectangle is also a common convention). A circle labeled A is an ammeter; one labeled V is a voltmeter. A diagonal arrow crossing an element’s symbol identifies a variable element.
Connections determine behavior. Every region joined by continuous ideal wire has one node potential. Components sharing both node endpoints are parallel even if far apart on the page. A circuit element can belong to more than one loop: a battery feeding two branches is part of a loop through either branch. Changing wire length or bending a schematic line without changing connections leaves the ideal circuit unchanged; connecting a new branch changes it.
Sketch conventional current unless the problem explicitly requests electron motion. Mark a connected junction with a dot; crossing lines without a connection do not imply a shared node. Label nodes and redraw when a crowded schematic hides the topology.
Open one branch, preserve another
A 6 V ideal battery connects nodes A (+) and B (−). One A-to-B branch contains bulb L1. A second A-to-B branch contains a switch in series with bulb L2. The switch opens. Describe current paths and voltage conditions.
Now place an ideal ammeter in the L2 branch and an ideal voltmeter across L2 only. Use the schematic below to track which connections the switch changes.
Identify A and B as the source nodes. Trace A→L1→B→battery→A, then A→switch→ammeter→L2→B→battery→A. The voltmeter is a separate connection across L2, with infinite resistance and no branch current.
Why this step? A connected schematic shows both closed load loops and the distinct measurement connections. Meter symbols alone do not determine correct placement.
Trace the two loops: battery–L1 and battery–switch–L2. The battery belongs to both.
Why this step? Loops are connectivity paths, not separate batteries.
Opening the switch breaks only the L2 branch. L1 still has a closed path and the battery’s 6 V across its endpoints.
Why this step? The other branch connects the same source nodes independently.
There is no steady current through L2. For a resistive unlit bulb with zero current, its voltage drop is zero, so the open switch gap supports the branch’s 6 V.
Why this step? A break stops flow but does not erase source voltage.
The ideal ammeter reads L2 current while the switch is closed and zero after it opens. With the switch open, the two L2 endpoints are at B potential, so the ideal voltmeter across L2 reads zero; the 6 V appears across the open switch instead.
Why this step? Ideal meters measure without changing the described connectivity. Zero current in L2 makes its own resistive voltage drop zero.
Answer and check
L1 remains on; L2 goes off. The source is shared by two possible loops, and the open gap can have nonzero voltage.
Series ammeter: L2 branch current. Parallel voltmeter: L2 voltage, which is zero when S is open. The open switch then carries the source voltage.
Make the model respond
Focused Physics 2 model
Two-resistor DC circuit
Predict first. Predict how total current changes when the same resistors are rewired in parallel.
Rₑq = R₁ + R₂; I₁ = I₂ = I; Vbattery = V₁ + V₂; P = I²R
On a narrow screen, scroll within a figure to read its labels. The table and explanation provide the same physics in text.
Series: I₁ = 0.2 A, I₂ = 0.2 A, and total current = 0.2 A.
Read the model data and comparisons
| Quantity | Value | Unit | Meaning or limit |
|---|---|---|---|
| Battery voltage | 12 | V | |
| Equivalent resistance | 60 | Ω | |
| Battery current | 0.2 | A | |
| R₁ current | 0.2 | A | |
| R₂ current | 0.2 | A | |
| R₁ voltage drop | 4 | V | |
| R₂ voltage drop | 8 | V | |
| R₁ power | 0.8 | W | |
| R₂ power | 1.6 | W | |
| Battery power | 2.4 | W | |
| Power residual Pbattery − P₁ − P₂ | -2.220 × 10^−16 | W |
In series, every resistor carries the same current, and the voltage drops sum to the battery voltage. In parallel, every branch has the full battery voltage, and the branch currents sum at the junction. In either topology, the ideal battery power equals the sum of resistor powers. The battery moves charge around a closed circuit; resistors transfer electric energy to thermal energy.
Assumptions and limits. Ideal constant-voltage battery, ideal wires, two ohmic resistors with fixed resistance and no temperature dependence. Steady DC state; conventional-current direction from the positive terminal. No internal battery resistance or transient behavior.
Try it from memory
Write your answer and reason before opening the worked answer. Your self-assessment is a study decision; it is not an automatically graded score.
Question 1
Two schematics have different-looking wire bends but connect every element to the same labeled nodes. Do they describe different ideal circuits?
Worked answer and reason
No. They have the same topology and therefore the same ideal behavior. A new junction or broken connection would change topology.
Physical connection relationships matter, not artistic layout.
Question 2
A 6 V ideal battery supplies a 2 Ω feed resistor in series with a 4 Ω load. An ideal wire is added across only the load. What happens to the load voltage and current, and what limits source current? Compare this with a finite-resistance shunt placed directly across an ideal fixed-voltage source.
Worked answer and reason
With the feed resistor retained, the load endpoints become the same node: load voltage and current are zero, while the feed carries 6/2 = 3 A and drops 6 V. A finite-resistance shunt directly across an ideal fixed-voltage source leaves that source-fixed load voltage and load current unchanged and adds extra shunt current.
An equal-potential shunt is valid only when the remaining circuit can satisfy both node and source constraints. Finite upstream resistance makes the intended bypass example consistent.
JavaScript enables saved drafts and self-assessment. You can always work on paper.
Catch the tempting mistake
- An open circuit has no voltage anywhere.
- It lacks a conducting path through the break, but sources and the open gap can have nonzero potential difference.
- Any two components drawn side by side are parallel.
- They must connect to the same two nodes.
Put it to work
Give the physical reason as well as the calculation. The worked solutions are on a separate page.
Scientific calculator workspace
Keep intermediate precision and report units. This calculator supports arithmetic and elementary functions.
Scientific calculator
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For the teacher
- Have students build one schematic then redraw it in two shapes.
- Use the symbol figure and require students to identify a variable-element arrow.
- Check the battery’s shared membership in both loops.
Source objectives and scope
- 11.2.A — Describe the behavior of a circuit.
Unless otherwise specified, all circuit schematic diagrams will be drawn using conventional current.
Suggested skills are teaching guidance. The course applies all science practices across its objectives.
Science references for this teaching
- College Board AP Physics 2 Course and Exam Description, Unit 11 (PDF pages 68–81) — Official topic order, learning objectives, all essential-knowledge clauses and boundaries. Equation pages 68,71,73,75,77–80 and relevant continuation pages visually inspected; independent reviewed-source-equation overlay consulted.
- OpenStax University Physics Volume 2, 9.3 Resistivity and Resistance — Independent verification of real material temperature dependence and the fixed-temperature qualification for linear metallic response. Teaching and assessment prose are original.
- OpenStax University Physics Volume 2, 10.3 Kirchhoff’s Rules — Independent verification of conservation-based branch and loop analysis; no calculus is needed in these authored tasks.
- Corrected original reading: Current and Resistance — Follow charge-flow rate and conventional-current direction; keep electron drift opposite the arrows.Supporting context; original AP teaching and practice above remain independently authored.
- Corrected original reading: Introduction to Circuits — Practice node connectivity, switches and common symbols. Check that any short-circuit idealization retains a finite current-limiting resistance.Supporting context; original AP teaching and practice above remain independently authored.
- Corrected original reading: Resistors in Circuits — Connect resistor voltage and current to energy transfer per second. Brightness comparisons require a stated bulb model.Supporting context; original AP teaching and practice above remain independently authored.
- Corrected original reading: Kirchhoff’s Laws — Trace actual closed paths and keep signed voltage changes. Use independent equations rather than combining disconnected branches into one loop.Supporting context; original AP teaching and practice above remain independently authored.
- Corrected original reading: Capacitors in Circuits — Compare equal-charge series and equal-voltage parallel capacitor arrangements.Supporting context; original AP teaching and practice above remain independently authored.
- Corrected original reading: RC Circuits — Use initial and long-time states, τ and qualitative curves. Source exponential and logarithmic transient calculations extend beyond required AP Physics 2 modeling.Supporting context; original AP teaching and practice above remain independently authored.
Glossary and deeper reading · 13 refreshers
These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.
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Short circuit
A short circuit provides a very low-resistance path between nodes that would otherwise have a potential difference. It can bypass components and draw a large current limited by the real source and wiring resistance. For example, a wire directly across an ideal resistor can bypass that resistor; a real battery short can heat the wiring dangerously.
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Electric current
Electric current is the net rate of charge flow through a specified cross section. It is measured in amperes, or coulombs per second, with direction defined by positive-charge motion. For example, the same steady current passes through each element of a simple unbranched series loop.
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Conventional current
Conventional current points in the direction that positive charge would move through a circuit. In a metal wire, electrons usually drift in the opposite direction. For example, a current arrow pointing right in a metal wire does not mean the conduction electrons drift right.
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Potential difference
Potential difference is the change in electric potential between two locations. It represents electric potential-energy change per unit charge and is measured in volts. For example, the potential difference across a resistor describes the energy transferred per coulomb passing through it.
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Heat
Heat is energy transferred between systems because of a temperature difference. It describes a transfer rather than a substance or energy store contained in an object. For example, when a warmer mug transfers energy to a cooler hand, the mug loses internal energy and the hand gains it.
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Capacitor
A capacitor stores energy by separating charge between conducting regions. In the ideal two-plate model, opposite plate charges create a potential difference related to charge by the capacitance. For example, disconnecting a charged capacitor from a battery leaves energy stored until a discharge path is provided.
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Electric charge
Electric charge is a conserved property that determines electric interactions. It can be positive or negative and is measured in coulombs; ordinary net charges arise from an imbalance of charged particles. For example, transferring electrons between initially neutral objects leaves one negatively charged and the other positively charged.
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Electrical resistance
Electrical resistance relates the potential difference across an element to the current through it. It is measured in ohms and depends on the element’s material, geometry, and conditions. For example, a longer uniform wire has greater resistance when cross-sectional area and material remain fixed.
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Electromotive force
Electromotive force is energy supplied per unit charge by a source or induction process. Despite its name it is measured in volts, rather than newtons, and can exist even when no current flows. For example, an ideal battery supplies an emf while an induced emf can be produced by changing magnetic flux.
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Internal resistance
Internal resistance models energy dissipation inside a real electrical source. When the source delivers current, its terminal voltage can be smaller than its emf because of this internal voltage drop. For example, connecting a heavy load to a battery can lower the voltage measured at its terminals.
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Ammeter
An ammeter measures current through a branch. It is connected in series with that branch and ideally has negligible resistance so it changes the current as little as possible. For example, inserting an ammeter into the wire leading to a resistor measures the current through that resistor.
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Voltmeter
A voltmeter measures potential difference between two nodes. It is connected in parallel and ideally has very high resistance so it draws negligible current. For example, placing its probes on opposite ends of a resistor measures that resistor’s voltage drop.
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Circuit node
A circuit node is a connected conducting region treated as having one potential in the ideal-wire model. Branches meet at nodes, so topology rather than the drawing’s shape determines how elements are connected. For example, moving a wire on a schematic without changing its connections leaves the circuit nodes unchanged.