Kirchhoff’s Laws

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# Kirchhoff’s Laws - PowerPoint PPT Presentation

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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Presentation Transcript

### 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.