Study Guide Exam 1

Closed book/Closed notes Bring a calculator Format – 6 short answer questions 3 questions on material from HW questions related to information presented in the lectures – 3 problems Equivalent Impedance/Admittance Nodal Analysis Mesh Analysis

Current The flow of positive charge through a cross- sectional area or the time rate of change of charge 1 Amp = 1 Couloub/second (A = C/s)

Voltage (Potential Difference) The electromotive force (emf) that causes charge to move 1 Volt = 1 Joule/1 Coulomb (V = J/C)

Power The change in energy measured in watts (W)

Conservation of Energy All power consumed by components must be generated by some other components within the circuit

Ohm’s Law V = I RV = I/G I = V/RI = V G Power dissipated by a component P = VI = V 2 /R = I 2 R

Equivalent ResistancesEquivalent Conductances In Series: R eq = R 1 + R 2 + R 3 ….+ R n G eq = [1/G 1 +1/G 2 +1/G 3 ….+ 1/G n ] -1 In Parallel: R eq = [1/R 1 +1/R 2 +1/R 3 ….+ 1/R n ] -1 G eq = G 1 + G 2 + G 3 ….+ G n

Kirchhoff’s Laws Kirchhoff’s Voltage Law (KVL) – Sum of all voltages in a loop is equal to zero Kirchhoff’s Current Law (KCL) – Sum of all currents at a node is equal to zero

Voltage Division: Resistances and Conductances The voltage across one resistor in a chain of multiple resistors in series is V R = [R/R eq ] V total V R = [G eq /G] V total where V total is the total of the voltages applied across the resistors.

Current Division: Resistances and Conductances The current flowing through one resistor in parallel with one or more resistors is I R = [R eq /R] I total I R = [G/G eq ] I total where I total is the total of the currents entering the node shared by the resistors in parallel.

Nodal and Mesh Analyses You will not be expected to find the values for voltages and currents in the circuit. You will have to draw the circuit with the voltages and currents labeled with appropriate markings for ground, polarity of the voltage, and direction of current flow as appropriate for the type of analysis. You will have to write the final set of questions after you have substituted the equations found using Ohm’s Law into the equations found using either Kirchhoff’s Voltage Law or Kirchhoff’s Current Law. – Through Step 5 in the step-by-step instructions shown in the next 2 slides.

Steps in Nodal Analysis 1. Pick one node as a reference node 2. Label the voltage at the other nodes 3. Label the currents flowing through each of the components in the circuit 4. Use Kirchoff’s Current Law 5. Use Ohm’s Law to relate the voltages at each node to the currents flowing in and out of them. 6. Solve for the node voltage 7. Once the node voltages are known, calculate the currents.

Steps in Mesh Analysis 1. Identify all of the meshes in the circuit 2. Label the currents flowing in each mesh 3. Label the voltage across each component in the circuit 4. Use Kirchoff’s Voltage Law 5. Use Ohm’s Law to relate the voltage drops across each component to the sum of the currents flowing through them. 6. Solve for the mesh currents 7. Once the voltage across all of the components are known, calculate the mesh currents.