Ohm’s Law and Simple Circuits Study Pack

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Last updated May 28, 2026

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Ohm’s Law and Simple Circuits Study Guide

Master the core relationships behind Ohm's Law — including I = V/R, resistivity, and power formulas like P = I²R — as you work through series and parallel circuits and compare ohmic versus non-ohmic materials.

Key Takeaways

  • Ohm's Law states that the current through a conductor equals the voltage across it divided by its resistance (I = V/R), and this relationship holds when temperature and other physical conditions remain constant.
  • Resistance is measured in ohms (Ω) and depends on a material's resistivity, its length, and its cross-sectional area — longer conductors and thinner wires have higher resistance.
  • In a series circuit, resistors share a single current path, so total resistance is the sum of individual resistances and the same current flows through every component.
  • In a parallel circuit, resistors provide multiple current paths, so total resistance is less than the smallest individual resistor and voltage is equal across every branch.
  • Electrical power dissipated by a resistor equals the product of voltage and current (P = IV), which can also be expressed as P = I²R or P = V²/R using Ohm's Law substitutions.
  • Ohmic materials produce a linear V–I relationship, while non-ohmic materials (such as diodes and filament bulbs) produce a curved V–I graph because their resistance changes with conditions.

Voltage, Current, and the Core Statement of Ohm's Law

Every circuit analysis begins with three fundamental quantities — voltage, current, and resistance — and the mathematical relationship that connects them.

Voltage (V)

  • Voltage is the electric potential difference between two points in a circuit, measured in volts (V); it is the 'push' that drives charge through a conductor.
  • A battery or power supply maintains a potential difference by doing work on charges, giving them energy that is later released in circuit components.

Current (I)

  • Current is the rate at which electric charge flows past a point, measured in amperes (A); one ampere equals one coulomb of charge per second.
  • Conventional current direction is defined as the direction positive charges would flow, which is opposite to the actual direction of electron movement.

Resistance (R)

  • Resistance is the opposition a material presents to the flow of current, measured in ohms (Ω); a resistance of 1 Ω allows 1 A of current when 1 V is applied.
  • Resistance arises at the atomic level when moving electrons collide with the lattice of atoms inside a conductor, converting electrical energy into thermal energy.

The Ohm's Law Equation

  • Ohm's Law is expressed as V = IR, where V is voltage in volts, I is current in amperes, and R is resistance in ohms.
  • Rearranged forms — I = V/R and R = V/I — are equally valid and allow any one quantity to be calculated when the other two are known.
  • The law applies only when resistance remains constant; it is a description of how many materials behave rather than a universal physical law.

Resistance and Material Properties

Resistance is not a fixed property of all materials — it depends on what a material is made of and the physical dimensions of the conductor.

Resistivity as a Material Property

  • Resistivity (ρ) is an intrinsic property of a material that quantifies how strongly it opposes current flow, measured in ohm-meters (Ω·m).
  • Good conductors such as copper and silver have very low resistivity (~1.7 × 10⁻⁸ Ω·m for copper), while insulators like rubber have resistivities many orders of magnitude higher.

Geometric Factors Affecting Resistance

  • The resistance of a conductor is calculated as R = ρL/A, where L is the length of the conductor and A is its cross-sectional area.
  • Doubling the length of a wire doubles its resistance because charges must travel through twice as many collision-prone atomic interactions.
  • Doubling the cross-sectional area halves the resistance because there are more parallel paths available for charge to flow through simultaneously.

Temperature Dependence

  • In most metallic conductors, resistance increases with temperature because higher thermal energy causes more frequent and energetic collisions between electrons and atoms.
  • Some materials called superconductors lose all electrical resistance below a critical temperature, allowing current to flow indefinitely without energy loss.

Ohmic and Non-Ohmic Materials

Not every circuit component maintains a constant resistance, and distinguishing between ohmic and non-ohmic behavior is essential for predicting how components will perform.

Ohmic Behavior and Linear V–I Graphs

  • An ohmic material maintains constant resistance regardless of the applied voltage, producing a straight-line graph when voltage is plotted on the y-axis and current on the x-axis.
  • The slope of the V–I line equals the resistance; a steeper slope indicates greater resistance.
  • Resistors used in most basic electronic circuits are designed to be ohmic across a specified operating range.

Non-Ohmic Behavior

  • A non-ohmic device has a resistance that changes depending on voltage, current, temperature, or other conditions, so its V–I graph is curved rather than straight.
  • A tungsten filament light bulb is non-ohmic because its resistance rises sharply as the filament heats up during operation.
  • A diode is a strongly non-ohmic semiconductor device that allows current to flow freely in one direction but blocks it in the reverse direction, making its V–I graph highly asymmetric.

Series Circuits: One Path for Current

In a series circuit, all components are connected end-to-end along a single conducting path, so the same current must pass through every element in sequence.

Current in a Series Circuit

  • Because there is only one path for charge to travel, the current I is identical at every point in a series circuit — it does not get 'used up' by each resistor.

Total Resistance in Series

  • The total or equivalent resistance of series resistors is simply the arithmetic sum: R_total = R₁ + R₂ + R₃ + …
  • Adding more resistors in series always increases total resistance, which reduces the total current drawn from the source.

Voltage Division in Series

  • The source voltage is divided among the resistors in proportion to their individual resistances; a resistor with twice the resistance of another will have twice the voltage drop across it.
  • The sum of all individual voltage drops across series resistors equals the total source voltage — this is a direct consequence of conservation of energy.

Practical Implication of Series Wiring

  • If one component in a series circuit fails (opens), the entire circuit breaks and no current flows through any component — the classic failure mode of old-style string Christmas lights.

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