# Derivatives and Integrals: An Annotated Discourse

### Worksheet33.2Networks Worksheet A4US

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#### Basic laws for electrical circuits.

This two-page worksheet was generously donated to the sample article by Virgil Pierce at a CuratedCourses workshop in August 2018. It has default (skinny) left and right margins, but we have specified longer top and bottom margins, with the top being the larger of the two.
##### Example33.7.Kirchoff’s Current Law.
For the circuit below $$I_1 + I_2 = I_3 \text{.}$$
Kirchoffs Current Law and Kirkoffs Voltage Law combined with Ohms Law gives for any circuit of resistors and sources a linear system that may (or may not) determine the currents.

#### 1.

For the simple network pictured, calculuate the amperage in each part of the network by setting up a system of linear equations for the amperages.

#### 2.

Compare it with a parallel circuit network. Calculate the amperage in each part of the network by setting up a system of linear equations for the amperages.

#### 3.

Now for a more complicated network. Calculate the amperage in each part of the network by setting up a system of linear equations for the amperages.

#### 4.

Now generalize these ideas to a context outside of electrical circuits. Consider the network of streets given in the diagram (with one-way directions as indicated).
A traffic engineer counts the hourly flow of cars into and out of this network at the entrances. They get (EB = East Bound; WB = West Bound):
Use a variable for each segment inside of the network and set up a system of linear equations restricting the flow. Solve the system. Note that you should not get a unique solution as traffic should be able to flow through the network in various ways.