ECSE 2170

Circuit Diagram Example

Node

Electrical conductor(s) or wires that connect two or more circuit elements.

Ordinary Node

An electrical connection point that connects only two elements.

Extraordinary Node

Node connected to three or more elements.

Ground Node

Node defined to be the zero-volts reference for the circuit.

Reference Node

Same as ground node (0 volts node)

Branch

The trace between two consecutive nodes containing one and only one element between them

Path

Any continuous sequence of branches, provided that no one node is encountered more than once

Loop

A closed path in which the start and end node are one and the same

Mesh

A loop that encloses no other loop

Planar Circuit

A circuit is planar if it is possible to draw it on a two-dimensional plane without having any two of its branches cross over or under one another (see figure below)

Non-Planar Circuit

If such a crossing is unavoidable, then the circuit is nonplanar

Series

Path in which elements share the same current. Series elements connect only at one end, never both ends. Rtotal = R1 + R2

Parallel

Path in which elements share the same voltage, which means they share the same pair of nodes (both ends) Rtotal = (1/R1 + 1/R2)^-1

Planar, R1 = 5 ohm and R2 = 6 ohm

Five, Five

All nodes in this circuit are extraordinary, No two single elements in this circuit are connected in series

Charge

The basic quantity in an electric circuit and is time dependent.

• Unit of charge = coulomb 

e = 1.6 x 10^-19

Current

The rate of change of charge

Two most common types of current

1. Direct Current (DC)

2. Alternating Current (AC)

24 ohms

Left:

Right:

Parallel and Series

a) 3600 V

A) 3 Parallel

B) 2 Series and 1 Parallel

C) 2 Parallel and 1 Series

D) 3 Series

I2 = 450 mA, I0 = 0 A

Right Side:

KCL:

37.5 V

Left:

Right:

Ohm’s Law

Kirchhoff’s Voltage Law (KVL)

Kirchhoff’s Current Law (KCL)

I1 = 4mA, I3 = 3 mA

Supernode

Formed by a voltage source (dependent or independent) connected between two non-reference nodes.

Steps of Mesh Analysis

1. Identify mesh (loops)

2. Assign a current to each mesh

3. Apply KVL around each loop to get an equation in terms of loop currents.

4. Solve the resulting system of linear equations for the mesh/loop currents

Mesh 1: I1 = 9A

Mesh 2: 2(I2 - I1) + 4(I2 - I3) = 0 

Mesh 3: 4(I3 - I2) + 8I3 + 40V = 0

Mesh 1:

Mesh 2:

Mesh 3:

Equ 1: I3 - I2 = 2 

Mesh 1 (Equ 2): -24V + 12I1 + 8(I1 - I2) + 20(I1 - I3) = 0

Super Mesh (Equ 3): 10I2 + 20I3 - 20(I3 - I1) + 8(I2 - I1) = 0

Equ 1: I3 - I2 = 2 

Mesh 1 (Equ 2):

Super Mesh (Equ 3):

a) 12 V, b) 7V, c) 0.25 A, d) -7 V

Vy = 7.517V, 207.167 mW = 207.167 mW (Pgenerated = Pabsorbed)

R1 = 200 ohms, R2 = 2k ohms

R1 = 1.875 k ohm, R2 = 3.75 k ohm, R3 = 7.5 k ohm, R4 = 15 k ohm

V = 18 V, 2A, -0.75