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EECE310 Lecture Notes (wk of 9-12-05)

# EECE310 Lecture Notes (wk of 9-12-05) - College of...

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Unformatted text preview: College of Engineering, Architecture, and Computer Sciences Department of Electrical and Computer Engineering Chapter 2 Direct Current (DC) Circuits EECE 310 Preston D. Frazier, Ph.D., P.E., PMP College of Engineering, Architecture, and Computer Sciences Department of Electrical and Computer Engineering Chapter 2-DC Circuits There are three basic laws that principally govern circuit analysis: 1) Ohm's Law 2) Kirchoff's Current Law (KCL) 3) Kirchoff's Voltage Law (KVL) EECE 310 Preston D. Frazier, Ph.D., P.E., PMP College of Engineering, Architecture, and Computer Sciences Department of Electrical and Computer Engineering Chapter 2-DC Circuits Ohm's Law states the voltage (v) across a resistance (R) is directly proportional to the current (i) flowing through it. Ohm's law is written as the following equation: v (t ) = Ri (t ) EECE 310 Preston D. Frazier, Ph.D., P.E., PMP College of Engineering, Architecture, and Computer Sciences Department of Electrical and Computer Engineering Chapter 2-DC Circuits Resistors are insulators, therefore conductors are in contrast to resistors. The voltage-current relationship for conductance (G) is: i (t ) v (t ) = G Conductance (G) is valued in Siemens (S). EECE 310 Preston D. Frazier, Ph.D., P.E., PMP College of Engineering, Architecture, and Computer Sciences Department of Electrical and Computer Engineering Chapter 2-DC Circuits To analyze electrical schematics, one must know the appropriate circuit terms. 1) Node a point of connection of two or more circuit elements. 2) Loop a closed path through a circuit in which no node is crossed more than once. 3) Mesh any loop that does not contain within it another loop. 4) Branch a portion of a circuit containing only a single element and nodes at each end of the element. EECE 310 Preston D. Frazier, Ph.D., P.E., PMP College of Engineering, Architecture, and Computer Sciences Department of Electrical and Computer Engineering Chapter 2-DC Circuits Kirchoff's Current Law (KCL) states the algebraic sum of the currents entering any node is zero (0). KCL is defined mathematically as: i (t ) = 0 j =1 j n is equal to the number of current flows EECE 310 Preston D. Frazier, Ph.D., P.E., PMP n College of Engineering, Architecture, and Computer Sciences Department of Electrical and Computer Engineering Chapter 2-DC Circuits The actual flow of the current in a particular circuit element is initially unknown. Therefore, a reference direction for the current is arbitrarily selected. This is usually distinguished with a positive polarity. Currents determined to be flowing in opposite directions will be opposite in sign. Current polarity is directly correlated to the voltage polarity. EECE 310 Preston D. Frazier, Ph.D., P.E., PMP College of Engineering, Architecture, and Computer Sciences Department of Electrical and Computer Engineering Chapter 2-DC Circuits Kirchoff's Voltage Law (KVL) states the algebraic sum of the voltages around any loop is zero (0). KVL is described mathematically as: v j =1 n j (t ) = 0 n is equal to the number of branch voltages EECE 310 Preston D. Frazier, Ph.D., P.E., PMP College of Engineering, Architecture, and Computer Sciences Department of Electrical and Computer Engineering Chapter 2-DC Circuits To ascertain currents and voltages in DC circuits, combining resistance (i.e., calculating equivalent resistance) is necessary. DC circuit schematics have three different configurations: 1) Series 2) Parallel 3) Series/Parallel Combination EECE 310 Preston D. Frazier, Ph.D., P.E., PMP College of Engineering, Architecture, and Computer Sciences Department of Electrical and Computer Engineering Chapter 2-DC Circuits If the current (i) flows through only one path to each resistor, then the resistors are designated to be in series. To calculate the equivalent resistance (Req) for a series combination, add all the values of the resistors. EECE 310 Preston D. Frazier, Ph.D., P.E., PMP College of Engineering, Architecture, and Computer Sciences Department of Electrical and Computer Engineering Chapter 2-DC Circuits Equivalent resistance (Req) for a series combination is stated as the following equation: n Req ( series ) = R j j =1 EECE 310 Preston D. Frazier, Ph.D., P.E., PMP n is equal to the number of resistors College of Engineering, Architecture, and Computer Sciences Department of Electrical and Computer Engineering Chapter 2-DC Circuits If the current (i) can flow through multiple paths, then the resistors within each path are characterized as being in parallel. To calculate the equivalent resistance (Req) for a parallel combination, add up the inverse values of each resistor and obtain the reciprocal of the summation. EECE 310 Preston D. Frazier, Ph.D., P.E., PMP College of Engineering, Architecture, and Computer Sciences Department of Electrical and Computer Engineering Chapter 2-DC Circuits Equivalent resistance (Req) for a parallel combination is given in the following equation: Req ( parallel ) 1 -1 = ( ) j =1 R j n n is equal to the number of resistors EECE 310 Preston D. Frazier, Ph.D., P.E., PMP College of Engineering, Architecture, and Computer Sciences Department of Electrical and Computer Engineering Chapter 2-DC Circuits Important Note about Parallel Resistance Configurations: - parallel; R 1 R 2 = ( R1 R 2 R 3 = ( 1 1 -1 R1 R 2 -1 R 1R 2 + ) =( + ) = R1 R 2 R 1R 2 R 1R 2 R1 + R 2 1 1 1 -1 R 1R 2 R 1R 3 R 2 R 3 -1 R 1R 2 R 3 + + ) =( + + ) = R1 R 2 R 3 R 1R 2 R 3 R 1R 2 R 3 R 1R 2 R 3 R 1R 2 + R 1R 3 + R 2 R 3 EECE 310 Preston D. Frazier, Ph.D., P.E., PMP College of Engineering, Architecture, and Computer Sciences Department of Electrical and Computer Engineering Chapter 2-DC Circuits The series/parallel configuration incorporates the two combinations in one schematic. As vast majority of the circuits that will be studied in this course will be of this type. To calculate the equivalent resistance (Req) for a series/parallel combination circuit will call for correctly evaluating the circuit in individual (series or parallel) configurations as segments to determine the total resistance (RT) in the network. EECE 310 Preston D. Frazier, Ph.D., P.E., PMP College of Engineering, Architecture, and Computer Sciences Department of Electrical and Computer Engineering Chapter 2-DC Circuits Configuration: Series varies constant R eq ( series ) = Parallel constant varies j Voltage (v = Ri) Current (i = v/R) Resistance R j =1 n Req ( parallel ) = ( j =1 n 1 -1 ) Rj n is equal to the number of resistors n is equal to the number of resistors EECE 310 Preston D. Frazier, Ph.D., P.E., PMP College of Engineering, Architecture, and Computer Sciences Department of Electrical and Computer Engineering Chapter 2-DC Circuits + VA RA + RA V - VA = T RA + RB + RC + VT - RB VB - RC VC = VT RA + RB + RC + VC RC - RB VB = VT RA + RB + RC Important Note about Voltage Divider Rule: Of the total voltage, the fraction that appears across a given resistance in a series circuit is the ratio of the given resistance and total resistance. EECE 310 Preston D. Frazier, Ph.D., P.E., PMP College of Engineering, Architecture, and Computer Sciences Department of Electrical and Computer Engineering Chapter 2-DC Circuits IT RB IA = IT RA RA + R B IA IB RB RA IB = IT RA + RB Important Note about Current Divider Rule: The rule only applies to two resistors in parallel. EECE 310 Preston D. Frazier, Ph.D., P.E., PMP College of Engineering, Architecture, and Computer Sciences Department of Electrical and Computer Engineering Chapter 2-DC Circuits Most of the schematics analyzed throughout this course will be rather arduous. To ascertain the parameters, current (i) and voltage (v), in DC circuits, several methodologies will be used. Each methodology will employ the three fundamental laws. EECE 310 Preston D. Frazier, Ph.D., P.E., PMP College of Engineering, Architecture, and Computer Sciences Department of Electrical and Computer Engineering Chapter 2-DC Circuits The techniques taught in this chapter will be: Node-Voltage Analysis Mesh-Current Analysis Superposition Principle Thevenin's/Norton's Theorem EECE 310 Preston D. Frazier, Ph.D., P.E., PMP College of Engineering, Architecture, and Computer Sciences Department of Electrical and Computer Engineering Chapter 2-DC Circuits The Node-Voltage (Nodal) Analysis is a great technique that can be applied to any circuit. To apply the procedure, the following steps must be taken: 1) One of the nodes in the circuit must be selected as the reference node. 2) Label the remaining nodes as voltage variables. 3) Use KCL and Ohm's Law to find the current flowing through each element. EECE 310 Preston D. Frazier, Ph.D., P.E., PMP College of Engineering, Architecture, and Computer Sciences Department of Electrical and Computer Engineering Chapter 2-DC Circuits Important Nodal Analysis Note: When a voltage source exists between two nodes, the voltage source and the two nodes can be written as a supernode. V1 VS = V2 VS = V1 V2 EECE 310 Preston D. Frazier, Ph.D., P.E., PMP College of Engineering, Architecture, and Computer Sciences Department of Electrical and Computer Engineering Chapter 2-DC Circuits EECE 310 Preston D. Frazier, Ph.D., P.E., PMP ...
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