Euclidean m-Space

1
Euclidean m-Space Linear Equations

• Electric Circuits and Pipe Networks

2
Direct Current Electric Circuits

• Consists of one or more electromotive forces
  (emf) and one or more resistors.
• Electromotive force, E, is measured in volts (V).
• Resistance, R, is measured in ohms (?).
• Current, I, is measured in amperes (A).

3
Ohms Law

• If I is the current in a simple circuit
  consisting of a single electromagnetic force (V)
  and a single resistance (R), then
• E IR.

4
Kirchhoffs Voltage Law

• In one traversal of any closed loop, the sum of
  voltage rises equals the sum of the voltage
  drops.
• That is, the algebraic sum of the voltage drops
  around any loop of the circuit is equal to the
  algebraic sum of electromotive forces in that
  loop.
• Note A loop is a closed path.

5
Kirchhoffs Current Law

• The sum of the currents flowing into any node is
  equal to the sum of the currents flowing out.
• That is, the algebraic sum of current at any node
  in a circuit is zero.
• Note A node is a point where three or more wires
  come together.

6
Example
7
Network Analysis Properties

• One Directional Flow At any instant, the flow in
  a branch is in one direction only.
• Flow Conservation at a Node The rate of flow
  into a node is equal to the rate of flow out of
  that node.
• Flow Conservation in the Network The rate of
  flow into the network is equal to the rate of
  flow out of the network.

8
Example
9
Homework 2.4