Kirchoff’s Voltage Law(KVL), first definition: In any closed loop the sum of the voltages is always equal to zero. Mathematical formula: VS - VR1 - VR2 - VR3 = 0 or VS = VR1 + VR2 + VR3 VS = Voltage Source VR1 = Voltage across R1 Circuit example:

EWB: Kirchoff’s Voltage Law(KVL), First Definition: 2 4 VS = VR1 + VR2 + VR3 12v = 2v + 4v + 6v 6

Treat each loop as a separate equation In Parallel, However Loop #1 Loop #2 Loop #3 Treat each loop as a separate equation

Kirchoff’s Laws I. Voltage Law A. Parallel--Voltage drop is the same across each “loop” B. Series 1. V(source) = V(sum of resistors)

Kirchoff’s Voltage Law(KVL), Second Definition: In any closed loop, the sum of the sources is equal to the sum of the voltage drops Mathematical formula: VS1 + VS2 = VR1 + VR2 + VR3 VS = Voltage Source VR1 = Voltage drop of R1 Circuit Example: Two sources

Kirchoff’s Laws I. Voltage Law A. Parallel--Voltage drop is the same across each “loop” B. Series 1. V(source) = V(sum of resistors) 2. V(sum of sources) = V(sum of resistors)

Kirchoff’s Current Law (KCL) Kirchoff’s Current Law is a mathematical expression of the balance of currents entering and leaving a node. A node is the intersection of more than two connectors. Kirchoff’s Current Law, first definition: The sum of all the currents entering and leaving a node is always equal to zero. Mathematical formula: IS = + I1 + I2 + I3 IS = current produced by source I1 , I2 , I3 = currents through users of energy, such as resistors

EWB: Kirchoff’s Current Law(KCL), first definition: Loop #1 Loop #2 Loop #3 Some current goes through each loop, more current goes through where there is less resistance

EWB: Kirchoff’s Current Law(KCL), first definition: 120 m 160 m 80 m I R3 I R1 I R2 360 m I S I S = I R1 + I R2 + I R3 360 ma = 120 ma + 80 mA +160 ma

Kirchoff’s Laws I. Voltage Law A. Parallel--Voltage drop is the same across each “loop” B. Series 1. V(source) - V(sum of resistors) = 0 2. V(sum of sources) = V(sum of resistors) II. Current Law A. Series--Current is the same across each resistor B. Parallel 1. I (total) = I (sum of loops)

EWB: Kirchoff’s Current Law(KCL), Second definition: In a node, the sum of the currents entering the node is equal to the sum of the currents leaving the node. Leaving NODE I 1 120 m 360 m 240 m I s I 2 I S = I1 + I2 Entering NODE NODE 360 ma = 120ma + 240ma

Kirchoff’s Laws II. Current Law I. Voltage Law A. Parallel--Voltage drop is the same across each “loop” B. Series 1. V(source) - V(sum of resistors) = 0 2. V(sum of sources) = V(sum of resistors) II. Current Law A. Series--Current is the same across each resistor B. Parallel 1. I (total) = I (sum of loops) 2. I (in) = I (sum going out)

Resistors Add in a Series Circuit A series circuit has only one loop or path for current flow R1 = 60 Ohms, R2 = 30 Ohms, R3 = 50 Ohms Total Resistance = 60 Ohms + 30 Ohms + 50 Ohms Total Resistance = 140 Ohms Total Current ( I ) = V/R (Ohm’s Law) = 140 volts / 140 ohms = 1 amp

Simplifying Resistance I. Series Circuit A. Total Resistance = Sum of resistors

In Parallel, the Resistors add up Inversely R1 = 100 Ohms, R2 = 150 Ohms, R3 = 75 Ohms 1/Total Resistance = 1/60 Ohms + 1/30 Ohms + 1/50 Ohms 1/Total Resistance = 0.0167 Ohms + 0.0333 Ohms + .02 Ohms 1/Total Resistance = 0.07 Ohms, Total Resistance = 14.3 Ohms

Simplifying Resistance I. Series Circuit A. Total Resistance = Sum of resistors II. Parallel Circuit A. 1/(Total Resistance) = 1/R(1) + 1/R(2) + ….