Electric Current Intensity, Series Circuits, and the Junction Rule (La Loi des Noeuds)

Experimental Objectives and Theoretical Principles

• Primary laboratory objectives:

  • Measure electric current intensity across various points in direct current (DC) circuits using an ammeter.
  • Experimentally verify and apply the junction rule (also known as the law of nodes or Kirchhoff's Current Law, la loi des noeuds).

• Fundamental concepts:

  • Electric current intensity ($I$): The rate of flow of electric charge through a conductive cross-section over time, quantified in amperes ($\text{A}$).
  • Ammeter configuration: An ammeter must always be connected in series with the branch or component being evaluated, allowing the entire charge flow of that pathway to pass through the measurement instrument.

Laboratory Equipment and Apparatus

• Essential components utilized in circuit construction:
  • DC generator / electrical power supply (générateur): Serves as the active source providing electromotive force and driving charge carriers through the closed circuit.
  • Connecting wires (fils de connexion): Conductive leads establishing low-resistance electrical connections between all circuit elements.
  • Switch (interrupteur, denoted as $K$): Controls circuit continuity by opening or closing the conductive loop.
  • Electric lamps (lampes, denoted as $L_1$ and $L_2$): Resistive loads converting electrical energy into light and thermal energy.
  • Receivers / resistors (récepteurs / résistors): Passive elements providing electrical load within the network.
  • Ammeters (ampèremètres, denoted as $A$): Measurement devices placed along circuit paths to determine the current intensity in amperes ($\text{A}$).

Series Circuit Analysis and Current Unicity

• Circuit configuration:

  • All components (DC power generator, switch $K$, ammeter $A$, lamp $L_1$, ammeter $A_1$, lamp $L_2$, and ammeter $A_2$) are connected sequentially end-to-end to form a single continuous closed conductive loop.
  • There are no branching paths or parallel junctions present in this setup.

• Experimental current measurements:

  • Initial / nominal measurement trial:
  • Main circuit current: $I = 0.8\,\text{A}$
  • Current entering first lamp $L_1$: $I_1 = 0.8\,\text{A}$
  • Current entering second lamp $L_2$: $I_2 = 0.8\,\text{A}$
  • Calibrated / precise measurement trial:
  • Main circuit current: $I = 0.78\,\text{A}$
  • Current through component branch 1: $I_1 = 0.78\,\text{A}$
  • Current through component branch 2: $I_2 = 0.78\,\text{A}$

• Conclusion and physical law (Law of Unicity):

  • In a series circuit, the electric current intensity is strictly identical at every point throughout the circuit loop:     $I = I_1 = I_2$
  • Physical basis: Due to the conservation of electric charge, charges cannot accumulate or escape within an unbranched conductive loop; the rate of flow leaving the positive generator terminal precisely equals the rate of flow through every component and back to the negative terminal.

Parallel Circuit Analysis and the Junction Rule

• Topological definitions:
  • Node / junction (noeud): An electrical connection point where more than two conductive branches meet. In the parallel circuit topology, points $A$ and $B$ constitute junctions.
  • Main branch (branche principale): The circuit pathway that contains the primary power generator and main control switch $K$.
  • Derived / parallel branches (branches dérivées): The independent secondary pathways connected between nodes $A$ and $B$, each containing its own load ($L_1$ or $L_2$) and dedicated ammeter.

• Experimental current measurements:

  • Total current flowing through the main branch: $I = 0.45\,\text{A}$
  • Current flowing through the first parallel branch (lamp $L_1$): $I_1 = 0.26\,\text{A}$
  • Current flowing through the second parallel branch (lamp $L_2$): $I_2 = 0.19\,\text{A}$

• Mathematical relationship and experimental verification:

  • Summation of parallel branch currents:     $I_1 + I_2 = 0.26\,\text{A} + 0.19\,\text{A} = 0.45\,\text{A}$
  • Verification of equivalence:     $I = I_1 + I_2$

• The Junction Rule (Loi des Noeuds):

  • General physical statement: The sum of the electric currents entering an electrical node is strictly equal to the sum of the electric currents leaving that node.
  • Mathematical expression:     $\sum I_{\text{entering}} = \sum I_{\text{leaving}}$
  • Application to Node $A$ (current-splitting node):
  • Entering current: $I$
  • Leaving currents: $I_1$ and $I_2$
  • Node equation:       $I = I_1 + I_2$
  • Application to Node $B$ (current-recombining node):
  • Entering currents: $I_1$ and $I_2$
  • Leaving current: $I$
  • Node equation:       $I_1 + I_2 = I$
  • Conservation principle: The junction rule is a direct macroscopic manifestation of the fundamental law of conservation of electric charge, confirming that electrical nodes cannot generate, destroy, or store net electric charge.