ELEC 105 Fundamentals of Electrical Engineering Spring 2010Review Topics for Exam #2The following is a list of topics that could appear in one form or another on the exam. Not all of these topics will be covered, and it is possible that an exam problem could cover a detail not specifically listed here. However, this list has been made as comprehensive as possible. You should be familiar with the topics on the previous review sheet in addition to those listed below.Dependent voltage sources- voltage is determined by a voltage or current elsewhere in circuit; the controlling voltage or current is always multiplied by a constant (the “gain”)- as with indep. voltage sources, current is unconstrained but instead determined by circuit external to source- equiv. to a short circuit (0 V) if controlling quantity is zeroDependent current sources- current is determined by a voltage or current elsewhere in circuit; the controlling voltage or current is always multiplied by a constant (the “gain”)- as with indep. current sources, voltage is unconstrained but instead determined by circuit external to source- equiv. to an open circuit if (0 A) controlling quantity is zeroNodal analysis- based on KCL applied to all nodes except reference node- node definition: not just a “dot;” includes wires and other conductors connected to dot(s)- definition of node voltage: voltage measured between a node and the reference node (ground); positive side at node, negative side at reference node- currents through resistors are expressed in terms of node voltages using Ohm’s law- a voltage source between non-ref. node and ground establishes the value of that node voltage; a KCL eqn (nodal eqn) is not necessary for that node- supernode required if indep. or dep. voltage source is connected between two non-reference nodes (a “floating” voltage source)o a supernode is a combination of two (or more) nodes; it encompasses the voltage source(s) and the nodes it (they) is(are) connected too apply KCL to supernode; must account for all circuit branches entering all nodes in the supernodeo the difference between the two node voltages in the supernode is equal to the voltage source connected between them (this is a KVL eqn, and it replaces the nodal eqn that is “lost” when the nodes are combined)- treatment of dependent sourceso surround dependent voltage sources not connected to ref. node with supernodes, just as with indep. voltage sourceso dependent current sources treated the same as indep. current sources in KCL eqno controlling voltages/currents must be expressed in terms of node voltages- nodal equations should have only node voltages as unknowns- in general, the solution of a system of simultaneous equations is required (for N nodes, there are N−1 independent equations in N−1 unknowns)- nodal equations should be manipulated into “standard form”o facilitates matrix solutiono terms involving unknowns (node voltages) on left-hand side in same order1o terms involving known quantities (constants) on right-hand sideThévenin and Norton equivalent circuits-TEC and/or NEC is associated with a specific set of terminals; a different set of terminalsin the same circuit has a different TEC/NEC-portion of circuit for which TEC/NEC being found is the “internal” (or modeled) circuit; the rest is the “external” circuit; that is, the internal circuit is treated as a “black box”-open-circuit voltage (voc) is evaluated at terminals with external circuit removed-short-circuit current (isc) flows through short between terminals with external circuit removed-a TEC/NEC “seen” by a device models the part of the circuit that does not include the device-polarity of voc vs. direction of isc-Thévenin equivalent voltage: vth = voc-Norton equivalent current: iN = isc-Thévenin and Norton equivalent resistances, Rth = RN = voc / isc = vth / iN-Thévenin (Norton) resistance can be found via three possible methods:oFind voc and isc and then evaluate the ratio Rth = RN = voc / iscoIf no dependent sources are present, deactivate all independent sources (replace voltage sources with shorts and current sources with opens), and find Req of the circuit using series/parallel combination formulasoIf dependent sources are present, deactivate all independent sources, apply a test source (vt or it), and evaluate the ratio Rth = RN = vt / itWheatstone bridge-balanced condition: voltage across “bridge” is zero; no current flows through “bridge”-enhances difference between variable voltage divider (like two strain gauges) on one side of bridge and “static” (unchanging) voltage divider on other side of bridge; improves detection of small voltage differencesSuperposition and linearity- two conditions of linearityo the response (a given circuit voltage or current) to a sum of inputs (stimuli, or independent voltage or current sources) is equal to the sum of the individual responseso if an excitation (stimulus, or independent voltage or current source) is scaled by a constant K, then the response (the part of a voltage or current due to that source) is also scaled by K- a definition of linearity: The portion of a voltage or current somewhere in a circuit due toa specific independent voltage or current source is directly proportional to the value of that source.- principle of superposition: Any voltage or current in a circuit is a weighted sum of the contributions from the individual independent sources driving the circuit. Stated another way, any voltage or current in a circuit can be expressed as a linear combination of independent voltage and current source values.- only applies if all circuit components have linear voltage-to-current relationships. These kinds of components include:o all independent sources (voltage or current)o dependent sources (voltage or current) with constant gain parameterso resistors, capacitors, and inductors2- procedure to apply superposition:o activate one independent source at a time; deactivate all others (i.e., replace indep.voltage sources with shorts and indep. current sources with opens)o leave dependent sources aloneo find desired voltage(s) and/or current(s) due to the active sourceo repeat the above 3 steps for each individual independent source in the circuito add together the components of the desired voltage(s) and/or current(s) due to the individual sources to find the actual (total) voltage(s) and/or currents(s) that results when all of the sources