Kirchhoff’s Law

Kirchhoff's Laws

  • Ohm’s Law and Resistor Values

    • R1 = 47.00 Ω

    • R2 = 0.27 kΩ (or 270 Ω)

    • R3 = 0.12 kΩ (or 120 Ω)

    • R4 = 47.00 Ω

    • R5 = 1.00 kΩ (or 1000 Ω)

  • Basic Circuit Components

    • Total Voltage (V_total) = 6 V

    • Total Current (Itotal) = 8 A

Conventional Current vs. Electron Flow

  • Conventional Current: Direction of current flow from positive to negative terminal (positive charge flow).

  • Electron Flow: Actual flow of electrons, which is from negative to positive terminal.

  • Recommendation: Use conventional current for calculations as it simplifies analysis and understanding.

Kirchhoff’s Laws

  • Gustav Kirchhoff (1845)

    • Fundamental laws in electrical engineering for circuit analysis.

Kirchhoff's Current Law (KCL)

Definition: The total current entering a junction must equal the total current leaving the junction.


Kirchhoff's Voltage Law (KVL)

Definition: The sum of the potential differences (voltage) across all elements in a closed circuit loop must equal zero.

Problem Solving Steps with Kirchhoff's Laws

  1. Assign Direction to Currents: Choose direction for currents in each wire; if uncertain, can be adjusted later if the sign of the current is negative.

  2. Apply KCL (Kirchhoff's Current Law): Set up equations based on the junctions.

  3. Draw a Loop for KVL (Kirchhoff's Voltage Law): Analyze closed loops in the circuit and establish equations.

  4. Determine Voltage Drops: If the assumed loop direction aligns with current, resistor voltage drop is considered negative.

  5. Determine Voltage Gains: If the loop goes against current direction, voltage is considered positive.

  6. Capacitor/Battery Behavior:

    • Leaving positive terminal = positive contribution to the loop equation.

    • Leaving negative terminal = negative contribution to the loop equation.

Example Problems (Practice Problems)

Example 1

  • Task: Find the current through each resistor

  • Solution: I = -0.33 A

    • Interpretation: Negative current indicates wrong initial assumed direction; adjust as necessary.

Example 2

  • Task: Find potential difference between points a and b (moving clockwise).

    • Given:

    • R1 = 5 Ω

    • R2 = 10 Ω

    • ε1 = 12 V

    • ε2 = 8 V

    • Capacitance = 4 𝜇F, Stores = 12 𝜇C

    • Current (I) = 2 A

    • Solution: Vb - Va = 13 V

Example 3

  • Task: Calculate current through each resistor in the circuit:

    • Given: I1 = 2 A, I2 = 3 A, I3 = 1 A.

    • Detailed verification through Kirchhoff’s Laws and expected constraints on the circuit yields these values.