Current Flow and Distribution in Parallel Circuits

Fundamentals of Electric Current and Series Circuits

  • Definition of electric current:
    • Electric current is defined as a flow of electrical charge around a circuit.
  • Direction of physical charge flow versus conventional current:
    • In a physical circuit, electrical charge moves from the negative end of the cell to the positive end.
    • Scientists historically and conventionally draw the current flowing in the opposite direction, from the positive terminal to the negative terminal.
    • This established representation is formally designated as conventional current.
  • Measurement of electric current:
    • Current is measured using an instrument called an ammeter.
    • An ammeter is wired directly in-line (in series) within the circuit path through which the charge flows.
  • Characteristics of a series circuit:
    • A series circuit contains no branches.
    • Because there are no junction points or alternate paths, electrical current can only flow along one single path.
    • The current is identical at all points around a series circuit.

Structure and Current Distribution in Parallel Circuits

  • Definition of a parallel circuit:
    • A parallel circuit is an electrical circuit that contains branches.
  • Splitting of current across branches:
    • Due to the presence of branches, the total current does not follow a single pathway; instead, the current splits.
    • Portions of the total electrical current pass through each of the separate branches of the circuit.
  • Conservation of charge in parallel circuits:
    • The total current leaving the electrical cell equals the sum of the separate currents flowing through the individual branches.
    • When the separate branch currents rejoin before returning to the power source, the combined current equals the original total current leaving the cell.
    • Key scientific rule:     Total Current Leaving Cell=∑Current in Branches\text{Total Current Leaving Cell} = \sum \text{Current in Branches}

Experimental Demonstration of Current Flow in a Parallel Circuit

  • Circuit arrangement and measurement points:
    • An ammeter placed immediately after the cell measures the total supply current leaving the cell.
    • Individual ammeters are connected within each parallel branch (upper branch and lower branch).
    • An ammeter placed on the return line measures the total current returning to the cell.
  • Observed quantitative data:
    • Current leaving the cell:     0.3 amp0.3\,\text{amp}
    • Current flowing through the upper branch:     0.1 amp0.1\,\text{amp}
    • Current flowing through the lower branch:     0.2 amp0.2\,\text{amp}
    • Combined current returning to the cell:     0.3 amp0.3\,\text{amp}
  • Quantitative verification:
    • Adding the branch currents demonstrates exact conservation:     0.1 amp+0.2 amp=0.3 amp0.1\,\text{amp} + 0.2\,\text{amp} = 0.3\,\text{amp}

Questions & Worked Examples

  • Example 1: Calculating Unknown Branch Current

    • Prompt / Scenario:
    • A parallel circuit has a total current leaving the cell of 0.5 amp0.5\,\text{amp}.
    • The current measured in the upper branch is 0.3 amp0.3\,\text{amp}.
    • Task: Calculate the current passing through the lower branch.
    • Principle:
    • The currents in the branches must add up to the total current leaving the cell:       Itotal=Iupper+IlowerI_{\text{total}} = I_{\text{upper}} + I_{\text{lower}}
    • Step-by-step calculation:     Ilower=Itotal−IupperI_{\text{lower}} = I_{\text{total}} - I_{\text{upper}}Ilower=0.5 amp−0.3 ampI_{\text{lower}} = 0.5\,\text{amp} - 0.3\,\text{amp}
    • Final value:     Ilower=0.2 ampI_{\text{lower}} = 0.2\,\text{amp}

  • Example 2: Calculating Total Supply Current

    • Prompt / Scenario:
    • A parallel circuit contains two branches.
    • The current measured in the upper branch is 0.4 amp0.4\,\text{amp}.
    • The current measured in the lower branch is 0.3 amp0.3\,\text{amp}.
    • Task: Calculate the total current leaving the cell.
    • Principle:
    • The total current leaving the cell equals the sum of the currents across all parallel branches:       Itotal=Iupper+IlowerI_{\text{total}} = I_{\text{upper}} + I_{\text{lower}}
    • Step-by-step calculation:     Itotal=0.4 amp+0.3 ampI_{\text{total}} = 0.4\,\text{amp} + 0.3\,\text{amp}
    • Final value:     Itotal=0.7 ampI_{\text{total}} = 0.7\,\text{amp}

Determinants of Branch Current and Additional Resources

  • Determinants of current magnitude in branches:
    • The precise amount of current that moves through different branches of a parallel circuit depends on circuit properties such as the electrical resistance present in each branch.
  • Supplementary practice resources:
    • Additional practice problems and exercises regarding current distribution in parallel circuits are provided in the revision workbook from freesciencelessons.co.uk.