AP Physics C E&M- 11.2 Simple Circuits- Study Notes- New Syllabus
AP Physics C E&M- 11.2 Simple Circuits – Study Notes
AP Physics C E&M- 11.2 Simple Circuits – Study Notes – per latest Syllabus.
Key Concepts:
- Behavior of a Circuit
- Circuit Elements
Behavior of a Circuit
An electric circuit is a system of electrical loops that provide paths for charges to move. Circuits may contain elements such as wires, batteries, resistors, lightbulbs, capacitors, inductors, switches, ammeters, and voltmeters.
Closed Electrical Loop:
- A closed loop is a continuous conducting path through which charges may flow.
- For current to exist, the circuit must contain at least one closed loop connected to a potential source.
Types of Circuits:
- Closed Circuit: A circuit in which charges are able to flow because the loop is complete.
- Open Circuit: A circuit in which charges are not able to flow because the loop is broken (e.g., an open switch).
- Short Circuit: A circuit where charges are able to flow with essentially no resistance and no significant potential difference. – This can cause very large currents, overheating, or damage to components.
Multiple Loops and Elements:
- A single circuit element can be part of more than one electrical loop (e.g., in parallel circuits).
- The properties of the entire circuit depend on how the elements are arranged (series, parallel, or combinations).
Circuit Schematics:
- Circuits are commonly represented using schematics, diagrams that use standardized symbols to represent elements.
- Schematics make it easier to describe, analyze, and calculate circuit behavior.
Key Idea: The flow of current in a circuit depends on whether a closed conducting path exists and on the physical arrangement of the components within that path.
Example
A simple circuit contains a battery, a switch, and a lightbulb. Describe the behavior of the circuit when the switch is open and when the switch is closed.
▶️ Answer/Explanation
Open Switch: The circuit is open, so there is no closed path for charges. Current does not flow, and the lightbulb remains off.
Closed Switch: The circuit becomes closed, charges flow due to the potential difference of the battery, and the lightbulb glows.
Example
A battery is connected directly with a wire of negligible resistance (no resistor or load). What happens?
▶️ Answer/Explanation
Step 1: The wire creates a short circuit across the battery terminals.
Step 2: The resistance is nearly zero, so the current becomes extremely large according to \( \mathrm{I = \dfrac{V}{R}} \).
Step 3: The large current can overheat the wire and battery, potentially damaging the circuit.
Final Answer: A short circuit allows charges to flow without a potential difference, causing dangerously high current and possible damage.
Circuit Elements
Circuit elements are the building blocks of an electrical circuit. Each element has specific electrical properties and is represented in a circuit diagram by a standard symbol.
Common Circuit Elements and Their Properties:
Battery (or emf source):
- Provides an electric potential difference that drives current.
- Symbol: long line (positive terminal), short line (negative terminal).
- Emf (\(\mathcal{E}\)) is the energy supplied per unit charge.
Resistor:
- Opposes the flow of current and converts electrical energy into heat or light.
- Relation: \( \mathrm{V = I R} \).
- Symbol: zig-zag line (U.S. convention) or rectangular box (international convention).
Capacitor:
- Stores electric charge and energy in an electric field between its plates.
- Relation: \( \mathrm{Q = C V} \).
- Symbol: two parallel lines (or one curved, one straight for polarized capacitors).
Inductor:
- Stores energy in a magnetic field when current passes through it.
- Relation: \( \mathrm{V = L \dfrac{dI}{dt}} \).
- Symbol: coil of wire (looped lines).
Switch:
- Controls whether a circuit is open or closed.
- Open switch = no current; closed switch = current flows.
- Symbol: break in line with movable lever.
Ammeter:
- Measures current in a circuit.
- Connected in series with very low internal resistance.
- Symbol: circle with “A”.
Voltmeter:
- Measures potential difference across a circuit element.
- Connected in parallel with very high internal resistance.
- Symbol: circle with “V”.
Lightbulb (as a resistor):
- Converts electrical energy into light and heat.
- Symbol: circle with an “X” or filament inside.
Key Idea: The properties of an electric circuit depend on how these elements are arranged (series, parallel, or mixed). Each element plays a unique role in controlling current, storing energy, or measuring circuit properties.
Example
A circuit contains a battery, resistor, and switch in series. Describe what happens when the switch is closed and when it is open.
▶️ Answer/Explanation
Switch Open: The circuit is incomplete; no current flows through the resistor, so no energy is dissipated.
Switch Closed: The circuit is complete; current flows through the resistor according to \( \mathrm{I = \dfrac{V}{R}} \). The resistor dissipates electrical energy as heat.