Study Guide

Exam 1

Exam 1

• Closed book/Closed notes• Bring a calculator

• Format– 6 short answer questions

• 3 questions on material from HW 1-3• 3 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)

1t

to

idtQ

dt

dqi

Voltage (Potential Difference)

• The electromotive force (emf) that causes charge to move

• 1 Volt = 1 Joule/1 Coulomb (V = J/C)

dq

dwv

Power

• The change in energy measured in watts (W)

vidt

dq

dq

dwP

dt

dwP

Conservation of Energy

• All power consumed by components must be generated by some other components within the circuit

circuit ain

0p

Ohm’s Law

V = I R V = I/GI = V/R I = V G

Power dissipated by a componentP = VI = V2/R = I2 R

Equivalent Resistances Equivalent Conductances

In Series: In Series:

Req = R1 + R2 + R3….+ Rn Geq = [1/G1 +1/G2 +1/G3….+ 1/Gn] -1

In Parallel: In Parallel:

Req = [1/R1 +1/R2 +1/R3….+ 1/Rn] -1 Geq = G1 + G2 + G3….+ Gn

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

VR = [R/Req] Vtotal

VR = [Geq/G] Vtotal

where Vtotal 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

IR = [Req/R] Itotal

IR = [G/Geq] Itotal

where Itotal 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 node2. Label the voltage at the other nodes3. Label the currents flowing through each of thecomponents in the circuit4. Use Kirchoff’s Current Law5. Use Ohm’s Law to relate the voltages at eachnode to the currents flowing in and out of them.6. Solve for the node voltage7. Once the node voltages are known, calculate thecurrents.

Steps in Mesh Analysis

1. Identify all of the meshes in the circuit2. Label the currents flowing in each mesh3. Label the voltage across each component in thecircuit4. Use Kirchoff’s Voltage Law5. Use Ohm’s Law to relate the voltage drops acrosseach component to the sum of the currents flowingthrough them.6. Solve for the mesh currents7. Once the voltage across all of the components areknown, calculate the mesh currents.