Kirchhoff’s Laws

Laws of Conservation

Kirchhoff’s Current LawKirchhoff’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 LawKirchhoff’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 DivisionTo determine the voltage across each

resistor we use:

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

Parallel ResistorsThe 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 ConductanceIt 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 ConductanceThe equivalent conductance of series

resistors is obtained in the same manner as the resistance of resistors in parallel.

Current DivisionFor 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.