Current electricity

• Current in parallel circuits with branches of equal resistance


  • Kirchhoff's first law governs the amount of current that flows into and out of a junction
  • Current going into a junction = sum of currents coming out of the junction
  • Current leaving a cell = current returning to the cell
  • At a junction, the amount of current that flows through each path depends on the resistance of that path
  • If resistors in parallel are identical, the current is split equally between the branches
• Solving for current in parallel circuits with branches of equal resistance


  1. Write Kirchhoff's first law: current going in = sum of currents coming out

  2. Since resistors are identical, current is split equally: current in each branch = total current in / 2

  3. Substitute values to solve for current in each branch
• Current in parallel circuits with branches of different resistance

  • Kirchhoff's second law: sum of potential differences across components in a loop = EMF in that loop
  • If resistors have different resistance, the current is not split equally between the branches
• In a parallel circuit, the paths for current split and rejoin at junctions
• Parallel circuits have multiple paths for current flow, unlike series circuits which have only one path
• At a junction, the total current going in equals the total current going out (Kirchhoff's first law)
• The current that leaves a cell is equal to the current that returns to the cell
• The amount of current that flows through each path at a junction depends on the resistance of that path
• If the resistors in parallel are identical, the current is split equally between the branches
• Kirchhoff's second law states that the sum of the potential differences across components in a loop equals the EMF in that loop
• If the resistors have different resistance, the current is not split equally between the branches
• Kirchhoff's second law


  The sum of the emf in the loop is equal to the sum of the potential differences of the components in that loop
• Kirchhoff's second law


  1. Emf provided = Potential difference across first resistor

  2. Potential difference across second resistor + potential difference across third resistor
• Potential difference across each branch

  Constant and equal to the emf
• Resistance of a branch

  Inversely proportional to the current through that branch
• Resistance of a branch

  Directly proportional to the potential difference across that branch divided by the current through it
• Current through a branch

  Inversely proportional to the resistance of that branch
• Paths with greater resistances will allow less current to flow through and vice versa
• Kirchhoff's first law


  The sum of the currents going into a junction is equal to the sum of the currents going out of that junction
• Applying Kirchhoff's first law

  Current going into junction = Current through first branch + Current through second branch
• Resistance


  Potential difference across component / Current through component
• Current


  Potential difference across component / Resistance of component
• Current through first branch

  Potential difference across first branch / Resistance of first branch
• Current through second branch

  Potential difference across second branch / Resistance of second branch
• Potential difference across both branches is the same
• Ratio of current through second branch to current through first branch

  Second branch resistance / First branch resistance
• Current through first branch

  Two-thirds of total current
• Current through second branch


  One-third of total current
• If resistance of one branch is double the other, the current through it will be half as large