Engineering Fundamentals and Problem Solving, 6e


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1 Engineering Fundamentals and Problem Solving, 6e Chapter 17 Electrical Circuits Chapter Objectives Compute the equivalent resistance of resistors in series and in parallel Apply Ohm s law to a resistive circuit Determine the power provided to a DC circuit and the power used by circuit components Use Kirchhoff s laws to solve resistive networks Utilize mesh currents to solve resistive networks 2 1
2 Charge charge, q is the basic unit of electricity property of electrons & protons: attract each other (opposite charge ) or repel each other (same charge ) we will focus on the behavior of electrons fundamental unit of charge (SI system) = coulomb 1 electron holds a charge of q = x C 1 proton holds a charge of q = x C unit of current = ampere 1 ampere or 1 amp = 1 C / s flowing past a given point (usually within a wire) 3 Current current, i is the flow of charge / charge in motion the mechanism by which electrical energy is transferred send power from generation point consumption point send signals from transmission point reception point has direction and value i dq dt positive or negative, depending upon reference direction amount of charge that has passed a given point: t q i d direct current (DC) is constant over time 4 2
3 Voltage current may pass a point (enter/leave an element) in 2 directions energy must be expended to move charge voltage, v is the work required to move current through an element, per charge (e.g. from A to B) unit of voltage = volt = 1 J/C v dw dq voltage can exist even when no current is flowing potential higher voltage + terminal higher potential lower voltage terminal lower potential charge tends to flow from higher voltage to lower voltage 5 Simple DC Electric Circuit and Symbols 6 3
4 Ohm s Law first discussed by Georg Simon Ohm (German physicist) in a pamphlet describing voltage & current measurements V I R voltage across a conducting material is linearly proportional to the current flowing through that material constant of proportionality = the resistance of the material v i R unit of resistance = the ohm 1 W = 1 V/A linear resistor another idealization, but still a good approximation for many Engineering: elements Fundamentals (over certain and Problem ranges Solving, of 6e voltage, current) 7 Resistors in Series V 1 V 2 V 3 V T R R R R T
5 Resistors in Parallel V T R R R R T DC Electric Power P VI P V R 2 given in Watts P I 2 R 12 5
6 Kirchhoff s Laws Kirchoff s voltage law The algebraic sum of all the voltages (potential drops) around any closed loop in a network equals zero. V drops = 0 Kirchoff s current law 14 Kirchhoff s Laws Kirchoff s voltage law Kirchoff s current law The algebraic sum of all of the currents coming into a node (junction) in a network must be zero. I node =
7 Circuit Example 17.7 Given the following circuit, determine the currents I x, I y, and I z. 18 Circuit Example cont d From Kirchhoff s current law at point A I y = I x + I z From Kirchhoff s voltage law around left loop  I y (2) + 14 I x (4) = 0 Around right loop  I y (2) + 12 I z (6) = 0 Results in: I x = 2A, I y = 3A, I z = 1A 19 7
8 Mesh Currents A node is a specific point or location within a circuit where two or more components are connected. A branch is a path that connects two nodes. A mesh is a loop that does not contain any other loops within itself. Mesh currents Exist only in the perimeter of the mesh Selected clockwise for each mesh Travel all the way around the mesh 20 Mesh Current Example Write the mesh current equations for this circuit. V 1 V 2 V 1 I a R 1 (I a I b )R 3 = 0 V 2 (I b I a )R 3 I a R 2 =
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