AP Physics 2 Electric Circuits: Learning to Analyze Real Networks

Charge conservation (in circuits)

Principle that charge is not used up in circuit elements; it moves through the circuit, so current is constrained by conservation of charge.

Current (I)

Rate of flow of charge through a cross-section of a wire/component; I = ΔQ/Δt.

Potential difference / Voltage (ΔV)

Energy per charge transferred between two points in a circuit; ΔV = ΔU/q.

Resistance (R)

Measure of how strongly a component resists current for a given voltage (for ohmic behavior, relates by Ohm’s law).

Ohm’s law (for an ohmic resistor)

Relationship between voltage, current, and resistance: ΔV = IR (under the conditions where the resistor is ohmic).

Ideal wire assumption

In AP Physics 2 circuit analysis, wires are typically treated as having negligible resistance unless stated otherwise.

Series connection

Components connected end-to-end so the same current must pass through each; there is only one path for charge through that part of the circuit.

Parallel connection

Components whose ends connect to the same two nodes, creating multiple paths for charge; each branch spans the same two nodes.

Node (junction)

A connection point in a circuit where branches meet; used to determine true series/parallel relationships based on connectivity.

Series current rule

In a series path, the current is the same through each element: I1 = I2 = I3 = I.

Series equivalent resistance (Req)

For resistors in series, the equivalent resistance is the sum: Req = R1 + R2 + R3.

Voltage division in series

In series, each resistor’s voltage drop is ΔVi = I Ri, so larger resistors have larger voltage drops (with the same current).

Parallel voltage rule

In parallel, each branch has the same potential difference because both ends connect to the same nodes: ΔV1 = ΔV2 = ΔV.

Kirchhoff’s Junction Rule (KJR)

At a junction, total current entering equals total current leaving: ΣIin = ΣIout (conservation of charge).

Parallel equivalent resistance (Req)

For resistors in parallel: 1/Req = 1/R1 + 1/R2 + 1/R3.

Parallel equivalent resistance qualitative rule

The equivalent resistance of parallel resistors is always less than the smallest branch resistance.

Power in a circuit element (P)

Rate of energy transfer/conversion in a circuit element: P = IΔV.

Power form: P = I^2R

Power expressed using current and resistance (derived from P = IΔV and ΔV = IR); often most direct when current is known/same (e.g., series).

Power form: P = (ΔV)^2/R

Power expressed using voltage and resistance; often most direct when voltage is known/same (e.g., parallel).

Kirchhoff’s Loop Rule (KLR)

Around any closed loop, the algebraic sum of potential changes is zero: ΣΔV = 0 (conservation of energy).

Resistor sign convention in KLR

Traversing a resistor in the same direction as the assumed current gives a drop ΔV = −IR; opposite the assumed current gives a rise ΔV = +IR.

Ideal battery/emf (ℰ) sign convention in KLR

Crossing from negative to positive terminal is a rise (+ℰ); from positive to negative is a drop (−ℰ).

Ideal ammeter

Meter with negligible resistance placed in series to measure branch current without significantly changing it.

Ideal voltmeter

Meter with extremely large resistance placed in parallel to measure potential difference without drawing significant current.

Reduce-then-expand strategy (combination circuits)

Process: (1) identify series/parallel groups by nodes, (2) reduce step-by-step to an equivalent resistance, (3) find total current, (4) expand back to find individual currents/voltage drops; switch to Kirchhoff if not reducible.