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Kirchhoff’s Laws

Kirchhoff’s Laws. Laws of Conservation. Kirchhoff’s Current Law. Kirchhoff’s current law (KCL) states that the algebraic sum of currents entering a node (or closed boundary) is zero. The sum of the currents entering a node is equal to the sum of the currents leaving the node. KCL (cont.).

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Kirchhoff’s Laws

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  1. Kirchhoff’s Laws Laws of Conservation

  2. Kirchhoff’s Current Law • Kirchhoff’s current law (KCL) states that the algebraic sum of currents entering a node (or closed boundary) is zero. • The sum of the currents entering a node is equal to the sum of the currents leaving the node

  3. KCL (cont.) • For current sources combined in parallel, the current is the algebraic sum of the current supplied by the individual sources.

  4. Kirchhoff’s Voltage Law • Kirchhoff’s voltage law (KVL) states that the algebraic sum of all voltages around a closed path (or loop) is zero • Sum of voltage drops = Sum of voltage rises

  5. KVL (cont.) • For voltage sources connected in series, the combined voltage is the algebraic sum of the voltages of the individual sources.

  6. Series Resistors • The equivalent resistance of any number of resistors connected in series is the sum of the individual resistances.

  7. Voltage Division • To determine the voltage across each resistor we use: • The voltage is divided among the resistors in direct proportion to their resistances.

  8. Parallel Resistors • The equivalent resistance of two parallel resistors is equal to the product of their resistances divided by their sum.

  9. Parallel Resistors (cont.) • The equivalent resistance of N resistors in parallel is • Req is always smaller than the resistance of the smallest resistor in the parallel combination. • If the resistances are equal, simply divide by the number of resistors.

  10. Parallel Conductance • It is often more convenient to use conductance when dealing with parallel resistors. • The equivalent conductance of resistors connected in parallel is the sum of their individual conductances.

  11. Serial Conductance • The equivalent conductance of series resistors is obtained in the same manner as the resistance of resistors in parallel.

  12. Current Division • For two resistors in parallel, the resistors will have current

  13. Current Division (cont.) • The total current i is shared by the resistors in inverse proportion to their resistances. • If a current divider has N conductors in parallel, the nth conductor (Gn) will have current

  14. Examples • Find current io voltage vo in the circuit.

  15. Examples • Find v1 and v2 in the circuit.

  16. Examples • Find the currents and voltages in the circuit.

  17. Examples • Find Req by combining the resistors.

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