AP® Physics C: Electricity and Magnetism review sheet from Aim for Five (aimforfive.com/physics-c-em/units/11/11-2)
Unit 11 · Topic 11.2
11.2 Simple Circuits
A circuit is a complete loop that charge can flow around. This topic covers the parts of a circuit and their schematic symbols, and the difference between a closed circuit, an open circuit and a short circuit, which is the key to many qualitative questions.
Key terms
- closed circuit
- open circuit
- short circuit
- circuit schematic
- electrical loop
The parts of a circuit
A circuit schematic is a simplified drawing that shows how parts are connected, not where they sit in real life. Wires are straight lines, and an ideal wire has no resistance, so every point along one unbroken wire is at the same potential. You can stretch, bend or shorten a wire on a schematic without changing the circuit, as long as the connections stay the same.
The table below lists the standard parts you need to recognize.
A variable element, such as a variable resistor or capacitor, uses its usual symbol with a diagonal arrow drawn through it.
| Element | Schematic symbol | What it does |
|---|---|---|
| Battery (cell) | a long line and a short line side by side; the long line is the positive terminal | supplies an emf that raises the potential of charge passing through it |
| Resistor | a zigzag line | turns electrical energy into thermal energy |
| Light bulb | a circle with a loop or an X inside | a resistor that also gives off light |
| Capacitor | two parallel lines of equal length | stores charge and energy (11.8) |
| Inductor | a coil of loops | resists changes in current (Unit 13) |
| Switch | a short line hinged open or closed | opens or closes a path |
| Ammeter / voltmeter | a circle with A or V | measures current / potential difference |
Closed and open circuits
A closed circuit has an unbroken conducting path from one terminal of the source, through the elements, and back to the other terminal. Current can flow only in a closed circuit. A single trip around such a path is called an electrical loop. Many circuits have several loops, and one element can belong to more than one of them.
An open circuit has a break somewhere: an open switch, a cut wire or a burned-out bulb. No current flows in that path, so every element in series with the break goes dark, even if it's far from the break.
Here's a surprise: no current doesn't mean no potential difference. With an ideal battery and an open switch, there's no current, so there's no potential drop across any resistor. The battery's full emf appears across the gap in the switch.
Short circuits
A short circuit is a path with essentially no resistance, so there's no potential difference across it. When a wire connects two points of a circuit directly, those two points become the same potential.
Any element connected only between those two points now has zero potential difference across it and carries no current. The short skips those elements, but the rest of the circuit still works. Because the short removes resistance, the total resistance drops and the current from the battery usually rises, so elements outside the short often get brighter.
A short placed straight across an ideal battery would demand an unlimited current. A real battery's internal resistance (11.5) limits it, but the battery and wire get hot fast, which is why shorts are dangerous.
- Ask: is there a complete path? If not, no current in that path.
- Ask: are both ends of this element connected by a bare wire? If so, it's shorted out.
- Then redraw the circuit without the shorted or open parts and analyze what's left.
Worked examples
Try each one yourself first, then open the solution.
- Example 1Calculator allowed
Shorting one bulb
Two identical bulbs, A and B, are connected in series to an ideal battery. A wire is then connected from one terminal of bulb B to its other terminal. What happens to each bulb's brightness?
Show the solutionHide the solution
- Step 1: The new wire connects both ends of bulb B, so they're at the same potential. Bulb B has no potential difference across it and carries no current. B goes out.
- Step 2: The circuit is now just the battery and bulb A. Before, the battery's emf was split between two equal bulbs; now bulb A has the full emf across it.
- Step 3: Twice the potential difference across the same resistance means twice the current through A, so A uses more power and glows brighter.
Answer: Bulb B goes out and bulb A gets brighter
- Example 2Calculator allowed
Potential difference across an open switch (classic trap)
A 9.0 V ideal battery, a 100 Ω resistor and an open switch are connected in series. What is the potential difference across the resistor, and across the open switch?
Show the solutionHide the solution
- Step 1: The switch is open, so the circuit is open and the current is zero.
- Step 2: With no current, the potential difference across the resistor is . Both ends of the resistor are at the same potential.
- Step 3: Walk around the loop: the battery raises the potential by 9.0 V and the resistor changes nothing, so the whole 9.0 V must appear across the gap in the switch.
- Step 4: The trap is assuming no current means no voltage anywhere.
Answer: 0 V across the resistor and 9.0 V across the open switch
Common mistakes
- Thinking a short circuit disables the whole circuit. It skips only the elements it connects across; the rest still has current, often more than before.
- Assuming that a break far from a bulb doesn't affect it. Any break in series with the bulb stops its current.
- Assuming no current means no potential difference anywhere. The source's emf shows up across the break.
- Reading a schematic as a physical layout. Only the connections matter; two points joined by a plain wire are the same point electrically.
On the exam
- Bulb questions are common: a switch opens or closes, or a wire is added, and you rank brightness or say whether it increases, decreases or stays the same. Redraw the circuit first, then compare currents or powers.
- When you explain a change in words, name the chain of reasoning: the change in total resistance, then the change in current, then the change in each element's potential difference or power.
Connected topics
Videos
Check yourself
4 questions on 11.2 Simple Circuits. Pick an answer to see if you got it, and why.
Three identical bulbs are connected in series with an ideal battery. A wire with negligible resistance is then connected across the middle bulb. What happens to the bulbs?
Bulbs P and Q are on separate parallel branches connected directly across an ideal battery. A switch in Q’s branch is opened. What happens to bulb P?
A circuit has two junctions, X and Y, joined by three branches. The left branch contains an ideal battery. The middle branch contains resistor R₂. The right branch contains resistor R₃.
Described circuit
How many different closed loops in this circuit include resistor R₂?
The right branch is disconnected at X, so R₃ no longer carries current. What happens to the current in R₂?
0 of 4 answered