Kirchhoff s laws
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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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Kirchhoff s laws

Kirchhoff’s Laws

Laws of Conservation


Kirchhoff s current law

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

KCL (cont.)

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


Kirchhoff s voltage law

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


Kvl cont

KVL (cont.)

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


Series resistors

Series Resistors

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


Voltage division

Voltage Division

  • To determine the voltage across each resistor we use:

  • The voltage is divided among the resistors in direct proportion to their resistances.


Parallel resistors

Parallel Resistors

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


Parallel resistors cont

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.


Parallel conductance

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.


Serial conductance

Serial Conductance

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


Current division

Current Division

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


Current division cont

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


Examples

Examples

  • Find current io voltage vo in the circuit.


Examples1

Examples

  • Find v1 and v2 in the circuit.


Examples2

Examples

  • Find the currents and voltages in the circuit.


Examples3

Examples

  • Find Req by combining the resistors.


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