Circuit Basics

1. Review of Electrical Voltage and Current

Ohm's law:

Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equation that describes this relationship:



where I is the current through the conductor in units of amperes, V is the voltage measured across the conductor in units of volts, and R is the resistance of the conductor in units of ohms. More specifically, Ohm's law states that the R in this relation is constant, independent of the current. Ohm's law is an empirical relation which accurately describes the conductivity of the vast majority of electrically conductive materials over many orders of magnitude of current. However some materials do not obey Ohm's law, these are called non-ohmic. The law was named after the German physicist Georg Ohm, who, in a treatise published in 1827, described measurements of applied voltage and current through simple electrical circuits containing various lengths of wire.

In circuit analysis, three equivalent expressions of Ohm's law are used interchangeably:



A graphical version for you to remember:



We'll go through the examples as follows:









2. Complete the circuits to test the voltage at node Vout using the multimeter in (a) and test the current flows in the circuit in (b).



3. Find the voltages Vs and Vx and the current through R2 and R5 in each of the following circuits. Verify the hand calculations using LTspice.



4. What is the equivalent resistance of the marked area in the following circuit?






Tasks:
(Show the calculation process for the credit. Complete these problems on papers)

1. Work on the following problems: (50 points for each)