CIRCUIT THEORY CHAPTER 2 BASIC LAWS BASIC LAWS

CIRCUIT THEORY CHAPTER 2 BASIC LAWS

BASIC LAWS CHAPTER 2 2. 1 Ohm’s Law. 2. 2 Nodes, Branches, and Loops.

Resistance – the ability of a material to resist the flow of charge through it. Resistance is related to the physical dimensions and resistivity of a material as follows: A l where l = length of conductor (in cm) A = cross-sectional area of conductor = resistivity of the material (in cm)

2. 1 OHMS LAW (1) Georg Simon Ohm established that there is an algebraic relationship between voltage and current for a resistor. This is easily shown experimentally by varying the voltage across a resistor and measuring the current through it. (so 1 = 1 V/A) V = IR Passive Sign Convention: A resistor is a passive device (it can only absorb energy) so Ohm’s Law must use passive sign convention. Example: Calculate the current through the resistor shown below. _ + 75 V 2. 7 k I

Resistor Characteristics and Ohm’s Law is easily shown experimentally by varying the voltage across a resistor and measuring the current through it. The result is a plot of the “characteristics” for a resistor which show a linear relationship. I V Note that straight-line sections in I-V characteristics are often indicative of resistance.

Conductance: Conductance, G, is the inverse of resistance and is a measure of a device’s ability to allow the flow of charge through it. Resistance is used more commonly, but conductance is used on occasion.

Variable resistors: Two names are used for variable resistors: • potentiometer - Most common name (discuss other uses) • rheostat R R 1 k 1 k Symbols 15 T 12 T 1 T 1 T 10 T

8 Power absorbed by resistors: Resistors are passive devices and can only absorb power. Power can be calculated in three ways: Substituting Ohm’s Law into the equation above yields:

9 Examples of resistors: Carbon Resistors 7 W Ceramic Resistor Wirewound Resistor DIP Resistors

2. 2 NODES, BRANCHES AND LOOPS (1) 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. A network with b branches, n nodes, and L independent loops will satisfy the fundamental theorem of network topology:

2. 2 Nodes, Branches and Loops (2) Equivalent circuit Original circuit How many branches, nodes and loops are there? has five branches, namely, the 10 -V voltage source, the 2 -A current source, and the three resistors. has three nodes a, b, and c. A loop is a closed path formed by starting at a node, passing through a set of nodes, and returning to the starting node without passing through any node more than once. A loop is said to be independent if it contains a branch which is not in any other loop. Independent loops or paths result in independent sets of equations. Although one can identify six loops in Fig. , only three of them are independent