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Kirchhoff’s Laws

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Kirchhoff’s Laws

Laws of Conservation

- 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

- For current sources combined in parallel, the current is the algebraic sum of the current supplied by the individual sources.

- 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

- For voltage sources connected in series, the combined voltage is the algebraic sum of the voltages of the individual sources.

- The equivalent resistance of any number of resistors connected in series is the sum of the individual resistances.

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

- The equivalent resistance of two parallel resistors is equal to the product of their resistances divided by their sum.

- 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.

- 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.

- The equivalent conductance of series resistors is obtained in the same manner as the resistance of resistors in parallel.

- For two resistors in parallel, the resistors will have current

- 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

- Find current io voltage vo in the circuit.

- Find v1 and v2 in the circuit.

- Find the currents and voltages in the circuit.

- Find Req by combining the resistors.