# Kirchhoff’s Laws - PowerPoint PPT Presentation

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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

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.)

• 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 (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.)

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

### Series Resistors

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

### 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

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

### 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

• 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

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

### Current Division

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

### 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

• Find current io voltage vo in the circuit.

### Examples

• Find v1 and v2 in the circuit.

### Examples

• Find the currents and voltages in the circuit.

### Examples

• Find Req by combining the resistors.