1. BASIC LAWS Ohm’s Law Kirchhoff’s Law
Series resistors & voltage division
Parallel resistors & current division
Y - transformation

2. Ohm’s Law
Property of a material to resist a flow of current known as resistance
Mathematically,
- measured in ohms ()
- Resistivity of the material
- length of the material
- Cross section area of the material
V  i

3. Ohm’s Law
Ohms’s Law: A voltage across a resistor is directly proportional to the current flowing through a resistor
V  i
v  i
Constant of proportionality between v and i is the resistance, R ()
v = i R
Must comply with passive sign convention

4. Ohm’s Law
Fixed resistors
Wirewound type
carbontype type

5. Ohm’s Law
Variable resistors

6. Ohm’s Law
Two extreme values of resistance:
Short circuit
Open circuit

7. Ohm’s Law Conductance: reciprocal of resistance
- measured in siemens (S)
Conductance: ability of an element to conduct current

8. Ohm’s Law + V  i Power in a Resistor Always positive
Always absorbs power

9. Kirchhoff’s Law Network topology
A branch represents a single element such as a voltage source or a resistor.

10. Kirchhoff’s Law Network topology
A branch represents a single element such as a voltage source or a resistor.
A node is the point of connection between two or more branches.

11. Kirchhoff’s Law Network topology
A branch represents a single element such as a voltage source or a resistor.
A node is the point of connection between two or more branches.
A loop is any closed path in a circuit.

12. Kirchhoff’s Law Network topology
Two or more elements are in series if they exclusively share a single node and consequently share the same current
Two or more elements are in parallel if they are connected to the same two nodes and consequently have the same voltage across them
1 & 2 - parallel
10V & 4 - parallel
5 in series with (1 and 2  in parallel)

13. Kirchhoff’s Law Kirchhoff’s Current Law (KCL)
Kirchhoff’s current law (KCL) states that the algebraic sum of currents entering a node (or a closed boundary) is zero
Mathematically,

14. Kirchhoff’s Law Kirchhoff’s Voltage Law (KVL)
Kirchhoff’s voltage law (KVL) states that the algebraic sum of all voltages around a closed path (or loop) is zero.
Mathematically,