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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

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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