College of Engineering and TechnologyWentworth Institute of Technology

James McCusker PhDmccuskerj@wit.edux4799

Short Circuit Open Circuit

Branch (b): a single two-terminal element.

Node (n): the point of connection between two or more branches. Electrical potential doesn’t change in a node.

Loops: a closed path.

Independent loop (l): contains at least one branch which is not a part of any other independent loops.

Determine the number of branches (b), number of nodes (n) and number of independent loops (l)

Example 2.3

Series connection: If a node is only connected to two elements, the adjoining elements are in series connection. The same current flows through series elements.

Parallel connection:if two or more elements are connected to the same two nodes, they are in parallel connection. The same voltage is across parallel elements.

Law of conservation of charge KCL

The algebraic sum of the currents entering and leaving a node, or a region, of a network is zero.

or

Algebraic sum: “+” for current entering “-” for current leaving

Example 2.4 Determine the unknown currents.

2 mA

6 mA

9 mA

4 mA

7 mA

ab c

d

Law of conservation of energy KVL

The algebraic sum of all voltages around a closed path is zero.

Closed path: the path of searching for voltage change, not the requirement for establishing current. Start at any point on the path and return to the original staring point.

Direction: clockwise or counterclockwise. No need to follow the direction of current.

Algebraic sum: “+” for voltage rise, “-” for voltage drop.

NotationNotation

Ground Ground connection provides direct path for current to return

A common point of zero electrical potential, with respect to which the voltage at any other points of the circuit is measured

Single-subscript notation

Specifies the voltage at any point in a circuit with respect to ground.

+

-

Earth ground Chassis ground

+

-

NotationNotation

NotationNotation

Measure voltage specified with single-subscript notation

Hook up the “+” lead to the point of interest and the “–” lead to the ground

Measure voltage specified with double-subscript notation

Hook up the “+” lead to the firstsubscript and the “–” lead to the other.

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If a node is only connected to two resistors, the adjoining resistors are in series connection.

Principle of voltage divisionThe voltage across series resistors is divided among the resistors in direct proportion to their resistances.

Series Resistors and Voltage Series Resistors and Voltage DivisionDivision

14

If the two terminals of resistors are connected to the same two nodes, the resistors are in parallel connection.

Two special cases

Two parallel resistors

N parallel resistors of equal value

Parallel ResistorsParallel Resistors

15

Principle of current divisionThe current through parallel resistors is divided among the resistors in direct proportion to their conductances.

Two special cases

Two parallel resistors

N parallel resistors of equal value

Current DivisionCurrent Division

DualityDuality

Dual relationships between series and parallel networks

Resistance of series circuit Conductance of parallel circuit

Voltage/Current Current/Voltage

17

Example 2.13

+ _

+ _

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20

21

College of Engineering and TechnologyWentworth Institute of Technology