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Lecture #3. OUTLINE KCL; KVL examples Dependent sources. Using Kirchhoff’s Voltage Law (KVL). Use reference polarities to determine whether a voltage is dropped – with no concern about actual voltage polarities. Consider a branch which forms part of a loop:. – v 2 +. + v 1 _.

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Lecture 3
Lecture #3

OUTLINE

  • KCL; KVL examples

  • Dependent sources


Using kirchhoff s voltage law kvl
Using Kirchhoff’s Voltage Law (KVL)

  • Use reference polarities to determine whether a voltage is dropped – with no concern about actual voltage polarities

Consider a branch which forms part of a loop:

v2

+

+

v1

_

voltage

“drop”

voltage

“rise”

(negative drop)

loop

loop


Formulations of kirchhoff s voltage law
Formulations of Kirchhoff’s Voltage Law

(Conservation of energy)

Formulation 1:

Sum of voltage drops around loop

= sum of voltage rises around loop

Formulation 2:

Algebraic sum of voltage drops around loop = 0

  • Voltage rises are included with a minus sign.

    Formulation 3:

    Algebraic sum of voltage rises around loop = 0

  • Voltage drops are included with a minus sign.


A major implication of kvl
A Major Implication of KVL

  • KVL tells us that any set of elements which are connected at both ends carry the same voltage.

  • We say these elements are connected in parallel.

+

va

_

+

vb

_

Applying KVL in the clockwise direction,

starting at the top:

vb – va = 0  vb = va


Kvl example

v2

v3

+ 

+ 

2

1

+

+

+

va

vb

vc

-

3

KVL Example

Three closed paths:

b

a

c

Path 1:

Path 2:

Path 3:




Find v using KVL and KCL


+

Simplify a circuit before applying KCL and/or KVL:

Find I

I

R1

R1 = R2 = 3 kW

R3 = 6 kW

R3

R2

7 V

R4

R4 = R5 = 5 kW

R6 = 10 kW

R6

R5


Find Vx, Vy and Vz


Dependent Sources

A linear dependent source is a voltage or current source that depends linearly on some other circuit current or voltage.

We can have voltage or current sources depending on voltages or currents elsewhere in the circuit.


Here, the voltage V provided by the dependent source (right) is proportional to the voltage drop over Element X. The dependent source does not need to be attached to the Element X in any way.


The 4 Basic Dependent Sources is proportional to the voltage drop over Element X. The dependent source does not need to be attached to the Element X in any way.


Circuit with dependent source example 1
Circuit with Dependent Source Example 1 is proportional to the voltage drop over Element X. The dependent source does not need to be attached to the Element X in any way.


Example is proportional to the voltage drop over Element X. The dependent source does not need to be attached to the Element X in any way. 2


Find is proportional to the voltage drop over Element X. The dependent source does not need to be attached to the Element X in any way. i2, i1 and io


Exercise

i is proportional to the voltage drop over Element X. The dependent source does not need to be attached to the Element X in any way. D

20 W

10 W

+

200 W

2.4 A

80 V

+

5iD

Exercise


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