1. 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:

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

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

4. 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)

5. 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

6. 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)

7. 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

8. 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

9. 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 R I R I R3
360 ma
= 120 ma
+ 80 mA
+160 ma

10. 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)

11. 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

12. 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)

13. 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

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

15. 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 = Ohms Ohms Ohms
1/Total Resistance = 0.07 Ohms, Total Resistance = 14.3 Ohms

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