Series and Parallel Resistor Networks – Ohm's Law & Kirchhoff's Laws

A set of vocabulary flashcards covering key concepts from the lecture on series and parallel resistor networks, Ohm's law, and Kirchhoff's laws.

Ohm's Law

V = I × R; fundamental relation between voltage, current, and resistance for a resistor.

Series Circuit

Components connected end-to-end such that the same current flows through all of them; total resistance is the sum of individual resistances.

Parallel Circuit

Components connected across the same two nodes such that the voltage across each is the same; currents split among branches.

Current Divider

In a parallel network, current splits among branches inversely proportional to their resistances; equal resistors share current equally.

Voltage Divider

A network of series resistors that splits the input voltage proportionally to their values; voltage across a resistor can be found by V = I × R or by divider ratios.

Equivalent Resistance

The single resistance that would draw the same current from the source as the network; for series: Req = ΣR; for parallel: 1/Req = Σ(1/R_i).

Kirchhoff's Current Law (KCL)

The sum of currents entering a node equals the sum of currents leaving the node.

Kirchhoff's Voltage Law (KVL)

The sum of all voltage gains and drops around any closed loop equals zero.

Ammeter

Meter placed in series to measure current; ideal ammeter has zero resistance.

Voltmeter

Meter placed in parallel to measure voltage; ideal voltmeter has infinite resistance.

Internal Resistance of Meters

The meters' own resistance; ammeters are near zero, voltmeters are very high; meter placement can affect readings.

Ladder Network

A repeating series-parallel circuit pattern that is reduced step by step from one end to the other.

Bracketing (Series-Parallel Reduction)

Grouping parts of a circuit with brackets to identify and simplify series or parallel blocks.

Voltage Drop

The decrease in voltage across a resistor when current passes through it; in a loop, sum of drops equals the source voltage.

Node Voltage

The electrical potential at a junction relative to a reference node (ground); used in analyzing voltage division.

Current Distribution in Parallel (Identical Resistors)

If resistors are identical in parallel, the total current splits equally among them.

Short Circuit

A path of very low resistance that can shunt current away from other elements and potentially cause damage.

Oxidation and Conductivity

Oxidation at connectors increases resistance, reducing conductivity and potentially altering current paths.

Voltage Source vs Current Source

A voltage source maintains a fixed voltage; a current source enforces a fixed current through the circuit.

Zero-Ohm Path in Parallel

A path with negligible resistance; in parallel with others, it dominates current distribution unless other paths are also very small.

Voltage Divider Example (Two Resistors in Series)

With V_source across R1 and R2 in series, the voltages split proportional to their resistances (e.g., Vr1 = I × R1, Vr2 = I × R2).

Current through Series Resistors

In a series chain, the same current flows through every resistor.

Ohm's Law in a Divider Context

Use I = Vsource / Rtotal and then Vr = I × R for each resistor to find individual voltages.