I. Passive Sign Convention
The passive sign convention is a set of rules to help simplify analysis. If you keep in mind the simple circuit consisting of two elements where one is a source and the other is a resistor, it is easy to remember which one supplies power and which one absorbs power. Looking at the resistor again, think of this as a reference (power product is positive and current of positive magnitude is entering the positive terminal of the voltage drop. See below. If I and V are both positive quantities, the power product will be positive. If current changes direction OR if voltage changes polarity, the power product would be negative. If current changes direction
AND voltage changes polarity, the power product would be positive (two negative quantities).
These are the four possible scenarios. i
I
V
Determine the power absorbed or supplied by the elements.
Element 1: +2 A is entering the positive terminal so element 1 is absorbing power (2*6) = 12 W.
Element 2 : + 2 A is entering the positive terminal so element 2 is absorbing power (2*18) = 36 W.
24 V source : +2 A is entering the negative terminal so this element is supplying power = (24*2) = 48 W.
Note that the power absorbed is (12 + 36) or 48 W and is equal to the power supplied (48 W).
II. Kirchoff’s Laws
Named after German scientist Gustav Kirchoff, these laws are used to help analyze more complicated circuits.

a) Kirchoff’s Current Law (KCL) b) Kirchoff’s Voltage Law (KVL)
KCL: the algebraic sum of currents entering any node is zero (conservation of charge). A node is a point of connection of two or more elements. Can also be stated the sum of currents entering a node is equal to the sum of currents leaving a node.
Example: How many nodes in this circuit?
(a) (b)
There are three nodes in this circuit (3 points of connection). If it helps to identify nodes, redraw the circuit (b) collapsing the wires to more clearly show the nodes or (c) cross hatch the wire to more clearly show the nodes. In circuit analysis, it always helps to label the nodes.
(c)

An example:
When you have 3 nodes, you only need 2 equations. Let us write them at the non-reference nodes:
1) I
1
= I
2
+ 3 mA
2) 12 mA = I
1
+ 4 mA
I
1
= (12 - 4) mA = 8 mA and by substitution, I
2
= I
1
– 3 mA or I
2
= 5 mA
KVL: the algebraic sum of all voltages around any closed path is equal to zero. A closed path is one in which no node is encountered more than once.
Example:
We only have one closed path, can travel either clockwise or counterclockwise. It is conventional to write KVL in a clockwise direction.
KVL: -100 + V
1
+ 50 + V
2
= 0 (1); now simplify

-50 + V
1
+ V
2
= 0 (2)
What is V
1
? By Ohm’s Law (V = IR), V
1
= I*(1 Ω ) and V
2
= I*(2 Ω )
Passive sign convention is satisfied (positive current is entering positive voltage terminal which is required for a resistor that is absorbing power).
If you go back to equation (2): -50 + 1*I + 2*I = 0
3I = 50 and I = 50/3 = 16.7 A. Now easy to find V
1
, V
2
Find I, V bd
KVL in outer loop: -6 + V
1
+ 12 + V
2
= 0
Ohms Law : V
1
= 80k
Ω
(I) and
V
2
=40k
Ω
(I), so
6 + 120k
Ω
(I) = 0 or
I = -6/120k
Ω
= -0.05 mA
KVL in inner loop: -6 + V
1
+ V bd
= 0
V bd
= 6-80 k
Ω
(-0.05 mA) = 6-(-4) = 10 V .
Note that a negative current means that current is flowing in the direction opposite of the direction that it is defined. The negative current will give you a negative value for V
1
as well as for V
2
.