2 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
3 KCL (cont.)For current sources combined in parallel, the current is the algebraic sum of the current supplied by the individual sources.
4 Kirchhoff’s Voltage Law Kirchhoff’s voltage law (KVL) states that the algebraic sum of all voltages around a closed path (or loop) is zeroSum of voltage drops = Sum of voltage rises
5 KVL (cont.)For voltage sources connected in series, the combined voltage is the algebraic sum of the voltages of the individual sources.
6 Series ResistorsThe equivalent resistance of any number of resistors connected in series is the sum of the individual resistances.
7 Voltage Division To determine the voltage across each resistor we use: The voltage is divided among the resistors in direct proportion to their resistances.
8 Parallel ResistorsThe equivalent resistance of two parallel resistors is equal to the product of their resistances divided by their sum.
9 Parallel Resistors (cont.) The equivalent resistance of N resistors in parallel isReq 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.
10 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.
11 Serial ConductanceThe equivalent conductance of series resistors is obtained in the same manner as the resistance of resistors in parallel.
12 Current DivisionFor two resistors in parallel, the resistors will have current
13 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
14 ExamplesFind current io voltage vo in the circuit.