supch02

# supch02 - CHAPTER 2 BASIC LAWS List of topics for this...

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CHAPTER 2 - BASIC LAWS List of topics for this chapter : Ohm's Law Nodes, Branches, and Loops Kirchoff's Laws Series and Parallel Resistors Wye-Delta Transformations Applications OHM'S LAW Ohm's law states that the voltage across a resistor is directly proportional to the current flowing through the resistor. R i v = Problem 2.1 Given an incandescent light bulb rated at 75 watts and 120 volts, find the “hot” resistance and “cold” resistance of the light bulb. An incandescent light bulb is the most common source of light produced by electrical energy. A current is made to flow through a wire, called a filament. Since this wire has resistance, the wire absorbs power, so much so that it “glows” and gives off light. Ratings on these types of light bulbs are for steady-state operating conditions. So, we have 40 25 120 75 V P I = = = amps 192 40 25 120 I V R = = = ohms Hence, the “hot” resistance is 192 ohms . Most wire has what we call a positive thermal resistance characteristic; that is, as the wire temperature increases, the resistance increases. It is sufficient to say at this time that the “cold” resistance is less than 192 ohms . Problem 2.2 Solve for v, i, and R for the following : (a) 10 R = ohms and 2 i = amps (b) 5 R = ohms and 20 v = volts (c) 10 v = volts and 5 i = amps (d) 3 i = amps and 20 v = volts

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(a) = v volts 20 (b) = i amps 4 (c) = R ohms 2 (d) = R ohms 667 . 6 NODES, BRANCHES, AND LOOPS 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. Problem 2.3 [2.7] Determine the number of branches and nodes in the circuit in Figure 2.1. Figure 2.1 There are 7 elements, 1 dependent current source, 1 independent voltage source, and 5 resistors, which implies that there are 7 branches . There are 5 nodes as indicated by the dark circles and dark lines in the circuit below. 5 5 10 V 5 5 10 V
Problem 2.4 Identify all the nodes, branches, and independent loops in Figure 2.1. Figure 2.1 There are 8 nodes , as indicated by the dark circles and dark lines in the circuit below. There are 14 branches , 4 independent voltage sources and 10 resistors. There are 7 independent loops . Check. Does this satisfy the fundamental theorem of network topology? b = l + n – 1 = 7 + 8 – 1 = 14 YES!

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Problem 2.5 In Figure 2.0 , is there a loop? How many nodes are there? A loop is any closed path; therefore it is easy to say there is no loop. However, there really is a loop since there is an infinite resistance connecting the end terminals together. Thus, there is one loop . There are three nodes , one where the voltage source and resistor join and the two at the output terminals. In addition, there are three branches . The voltage source, the resistor, and the infinite resistance. Thus, the fundamental theorem of network topology is satisfied.
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