Skip to main content
Physics LibreTexts

4: Batteries, Resistors and Ohm's Law

  1. Last updated
  2. Save as PDF
  • Page ID
    5437

    • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    \( \newcommand{\dsum}{\displaystyle\sum\limits} \)

    \( \newcommand{\dint}{\displaystyle\int\limits} \)

    \( \newcommand{\dlim}{\displaystyle\lim\limits} \)

    \( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)

    ( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\id}{\mathrm{id}}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\kernel}{\mathrm{null}\,}\)

    \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\)

    \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\)

    \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    \( \newcommand{\vectorA}[1]{\vec{#1}}      % arrow\)

    \( \newcommand{\vectorAt}[1]{\vec{\text{#1}}}      % arrow\)

    \( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vectorC}[1]{\textbf{#1}} \)

    \( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)

    \( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)

    \( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)

    \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \(\newcommand{\longvect}{\overrightarrow}\)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    \(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)

    • 4.1: Introduction
      An electric cell consists of two different metals, or carbon and a metal, called the poles, immersed or dipped into a liquid or some sort of a wet, conducting paste, known as the electrolyte, and, because of some chemical reaction between the two poles and the electrolyte, there exists a small potential difference (typically of the order of one or two volts) between the poles.
    • 4.2: Resistance and Ohm's Law
      The conventional direction of the flow of electricity is the direction in which positive charges are moving. That is to say, electricity flows from the positive electrode towards the negative electrode. The positive ions, then, are moving in the same direction as the conventional direction of flow of electricity, and the negative ions are moving in the opposite direction.
    • 4.3: Resistance and Temperature
      This page explains the relationship between temperature and resistivity in metals and semiconductors. Metals experience increased resistivity with higher temperatures due to more collisions among conduction electrons, while semiconductors see a decrease in resistivity as more electrons become available for conduction. The temperature coefficient of resistance indicates these changes for various materials.
    • 4.4: Resistors in Series
      This page explains that in series circuits, total resistance is the sum of individual resistances, with current remaining constant throughout. It notes that the potential difference is greatest across the highest resistance, illustrating key concepts of Ohm's Law and circuit behavior.
    • 4.5: Conductors in Parallel
      This page explains the relationship between conductance and resistance in parallel circuits, highlighting that total conductance is the sum of individual conductances. It mentions that total resistance can be calculated for resistances in parallel. The page emphasizes that the potential difference is constant across components and that current flows predominantly through the component with the highest conductance, corresponding to the lowest resistance.
    • 4.6: Dissipation of Energy
      When current flows through a resistor, electricity is falling through a potential difference. When a coulomb drops through a volt, it loses potential energy 1 joule. This energy is dissipated as heat.
    • 4.7: Electromotive Force and Internal Resistance
      This page explores electromotive force (EMF) in a cell, defining it as the potential difference when no current is drawn. It illustrates how internal resistance impacts current through an example with a 2 V cell and a 4 Ω resistor. The total resistance includes both external and internal resistances, and the potential across the cell decreases when current flows, necessitating a redefinition of potential difference.
    • 4.8: Power Delivered to an External Resistance
      This page explains heat generation in an external resistance, noting that no heat is produced at zero or infinite resistance. It identifies an optimal resistance value for maximizing power output, defined by the formula \(P=I^2R=\frac{E^2R}{(R+r)^2}\). The maximum power transfer occurs when the external resistance matches the internal resistance of the source (i.e., \(R = r\)).
    • 4.9: Potential Divider
      A potential divider can be used to supply a variable voltage to an external circuit (where is called a rheostat) or it may be used to compare potential differences, in which case it is called a potentiometer.
    • 4.10: Ammeters and Voltmeters
      This page details the use of ammeters and voltmeters in circuit measurements, explaining that ammeters measure current in series with low resistance, while voltmeters measure potential difference in parallel, acting as high-resistance ammeters. It also covers multimeters as dual-purpose devices and provides guidance on calculating shunt resistances for high currents and series resistances for precise voltage measurements.
    • 4.11: Wheatstone Bridge
      The Wheatstone bridge can be used to compare the value of two resistances – or, if the unknown resistance is compared with a resistance whose value is known, it can be used to measure an unknown resistance.
    • 4.12: Delta-Star Transform
      This page explains the "delta" and "star" configurations in electrical circuits, detailing the relationship between resistances and conductances. It includes equations for converting between configurations, highlighting their electrical equivalence. The page suggests using programmed calculators for convenience in these transformations and presents an example problem that calculates the resistance between points in a circuit, resulting in a value of 2.85 Ω.
    • 4.13: Kirchhoff’s Rules
      This page explains Kirchhoff’s rules in electrical circuits, covering pronunciation and key principles. K1 states that the net current at a circuit point is zero, while K2 ensures the sum of EMFs and IR products is also zero in closed circuits. It provides a detailed process for applying these rules to a circuit with five resistors, including diagramming, marking unknown currents, and formulating equations, ultimately illustrating how to solve for the currents in the resistors.
    • 4.14: Tortures for the Brain
      I don’t know if any of the examples in this section have any practical applications, but they are excellent ways for torturing students, or for whiling away rainy Sunday afternoons.
    • 4.15: Solutions, Answers or Hints to 4.14
      This page covers electrical resistance problems, including the analysis of current in a cube of resistors and effective resistance calculations using Ohm's Law and Kirchhoff's rules. It presents specific effective resistance values, such as \(\frac{5}{6}r\) and \(1.52 \Omega\), and discusses heat generation in series and parallel configurations. Additionally, it explores the Fibonacci sequence in relation to resistance, detailing the formula \(R_n=\frac{F_{2n+1}}{F_{2n}}\).
    • 4.16: Attenuators
      This page explores resistor networks used as attenuators for educational purposes, detailing the design of T-type attenuators to adjust current and voltage between devices with specific internal resistances. It incorporates Kirchhoff’s rules and Ohm’s law to calculate needed resistance values. Additionally, it introduces various attenuator types—T, H, Pi, and square—alongside formulas for their resistance ratios based on the desired voltage reduction factor.

    Thumbnail: Basic Wheatstone bridge. (CC BY-SA 4.0 International; Daraceleste via Wikipedia)

    This page titled 4: Batteries, Resistors and Ohm's Law is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Jeremy Tatum via source content that was edited to the style and standards of the LibreTexts platform.