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Kirchhoff's Current Law

Jul 4, 2024

Kirchhoff's Current Law (KCL)

Basic Concept

  • Kirchhoff's Current Law (KCL): The total current flowing into a junction equals the total current flowing out.
  • Convention:
    • Currents flowing into the junction are positive.
    • Currents flowing out of the junction are negative.
  • Mathematical Representation: Sum of all currents at a junction = 0
    • Example: If 10A flows in and 10A flows out, 10 + (-10) = 0

Example 1

  • Drawing the setup: a junction with currents i1 (10A in) and i2 (4A out)
  • Determining Current Signs:
    • i1 = +10A (flowing into the junction)
    • i2 = -4A (flowing out of the junction)
  • Calculation for i3:
    • Equation: i1 + i2 + i3 = 0
    • 10 - 4 + i3 = 0
    • i3 = -6A (flowing out)
  • Verification:
    • Entering current: 10A
    • Leaving current: 6A + 4A = 10A

Example 2

  • Setup: a junction with currents i1 (10A in), i2 (14A out)
  • Determining Current Signs:
    • i1 = +10A
    • i2 = -14A
  • Calculation for i3:
    • Equation: i1 + i2 + i3 = 0
    • 10 - 14 + i3 = 0
    • i3 = +4A (flowing in)
  • Verification:
    • Entering current: 10A + 4A = 14A
    • Leaving current: 14A

Example 3

  • Setup: a junction with currents i1 (8A out), i2 (9A in), i3 (7A in)
  • Determining Current Signs:
    • i1 = -8A
    • i2 = +9A
    • i3 = +7A
  • Calculation for i4:
    • Equation: i1 + i2 + i3 + i4 = 0
    • -8 + 9 + 7 + i4 = 0
    • i4 = -8A (flowing out)
  • Verification:
    • Entering current: 9A + 7A = 16A
    • Leaving current: 8A + 8A = 16A

Example 4

  • Setup: a junction with currents i1 (12A in), i2 (8A out), i3 (unknown), i4 (2*i3), i5 (20A in)
  • Determining Current Signs:
    • i1 = +12A
    • i2 = -8A
    • i5 = +20A
    • i4 = 2*i3
  • Calculation for i3 and i4:
    • Equation: i1 + i2 + i3 + i4 + i5 = 0
    • 12 - 8 + i3 + 2*i3 + 20 = 0
    • 24 + 3*i3 = 0
    • i3 = -8A (flowing out)
    • i4 = 2 * (-8A) = -16A
  • Verification:
    • Entering current: 12A + 20A = 32A
    • Leaving current: 8A + 8A + 16A = 32A

Key Takeaways

  • KCL ensures that the sum of currents entering and leaving a junction is always zero, maintaining current balance.
  • Sign convention is crucial for correctly applying KCL.
  • Verification by adding entering and leaving currents helps ensure calculations are correct.*

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