Kirchhoff’s Current Law (KCL)
Kirchhoff’s Voltage Law (KVL)
The algebraic sum of all currents entering a node must always be zero
where i_{n} is the n^{th} current. N is the number of branches. A common assignment:
For the following figure The node equation can be written as To use KCL to analyze a circuit,

Example: Find the current through a 20Ω resistance, and current through a 40Ω resistance
Write in the circuit using Ohm’s Law
Apply last two equation into KCL at node x The current through a 20Ω resistance The current through a 40Ω resistance 
The algebraic sum of all voltage around the closed loop must be always zero.
where v_{n} is the n^{th} voltage. N is the number of elements in the loop A common assignment:
For the following figure To use KVL to analyze a circuit,

Example 2: Find the current i and voltage v over the each resistor.
Example 3: Find v1 and v2 in the following circuit
(note: the arrows are signifying the positive position of the box and the negative is at the end of the box)
Example 4: Find V1, V2, and V3.
(note: the arrows are signifying the positive position of the box and the negative is at the end of the box)
Example 5: Find V1, V2, V3,and V4
(note: the arrows are signifying the positive position of the box and the negative is at the end of the box)
(Click image to view solution)
Problem 1: Find V1 in the following circuit.
Problem 2: Find V0 in the following circuit.
Problem 3: Find V1,V2, and V3 in the following circuit.
Problem 4: Find I_{1},I_{2}, I_{3}in the following circuit
Problem 5: Find the resistor R value in the following circuit.