unit 2 voltage and current sources

8/10/2019 Unit 2 Voltage and Current Sources

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Electric Power

When electric current flows in a circuit with resistance, it does work.

- is the rate at which electrical energy is transferred by an electric circuit.

The SI unit of power is the watt .

Devices convert this work into many useful forms, such as heat (electricheaters), light (light bulbs), motion (electric motors) and sound (loudspeaker).

Electricity can be produced by generation or from storage such as batteries.

R

V Pand R I P

R

V I but VI P

22

==

==


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Two Types of Power

+

v

_

i

1. Power Absorbed

2. Power Generated

- the current arrow is directed into the + marked terminal ofan element.

-the current arrow is directed out of the + terminal of anelement.

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Example 1

Compute the power absorbed by each part of the circuit networks given below.

+

2V

_

3A

+

- 2V

_-3A

+

4V

_

-5A

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Example 2

a. Find the power being absorbed by the circuit element (a).

b. Find the power generated by the circuit element (b).

c. Find the power delivered to the circuit element (c) at t=5ms.

4.6A

220mV

+

-

(a)

-3.8V+

-

(b)

-1.75A

8e-100t

V +

(c)

3.2A

-

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s

Voltage and Current Sources

Circui t Symbols of the Independent Voltage Source

Circuit Symbols of the Independent Current Source

vs

s

V

DC Voltage Source Equivalent

vs

AC Voltage Source

DC Current Source Equivalent AC Current Source

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Voltage-Controlled Voltage Source

Current-Controlled Current Source

Dependent Sources

Voltage-Controlled Current Source

Current-Controlled Voltage Source

K x gv x

Kvx r x

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Example 3

In the circuit below, if v 2 is known to be 3V, find v L .

5v 2v 2+

-

v L

+

-

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Find the power absorbed by each element in the circuit shown below.

Example 4


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Path is the set of nodes and elements that are passed through once.

Example 5:

How many nodes and branches can be found in the given circuits below?

Branch is a single path in a network composed of one simple elementand the node at each of that element.

Node is a point which two or more elements have a commonconnection.

Loop is a path created if the node started ends at the same node.

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Example 6

In the given circuit below, determine the following:

a. The number of nodes

b. The number of branches

c. If we move from A to B to E to D to C to B, have we formed a path? A loop?


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Example 7

18V vxR A 6

5 13A

x

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Kirchhoff s Laws

These laws are used to solve complex circuits.

Complex circuits are those in which there is more than one EMF in thecircuit or the resistors are connected in a complex manner.

So simplification cannot be done by series and parallel circuit rulesand Ohms law cannot be applied.


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Two Kirchhoffs laws

. Kirchhoffs Current Law (KCL)1

It states that, the algebraic sum of the currents meeting at a junction in an electrical circuit is zero.

This law is also known as the Junction Rule.

A junction is that point in an electrical circuit where three or morecircuit elements meet.

I1I2

I3

I4 I5

. Kirchhoffs Voltage Law (KVL)2

. Kirchhoffs Current Law (KCL)1


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Problems on KCL

Using KCL find the currents I 1, I2, I3, I4, I5 in the given electric circuit below.

Example 8


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Example 9

For the circuit below, compute the current through resistor R 3 if it isknown that the voltage source supplies a current of 3A.

10V R2

R1

R3 5A

2A

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c. If x=3A and the 18-V source delivers 8A of current, what is the value of R A?

18V vxR A 6

5 13A

x

Example 10 Page 32


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. Kirchhoffs Voltage Law (KVL)2

It states that, in any closed electrical circuit or mesh, the algebraic sum ofall the electromotive forces (EMFs) and voltage drops in resistors is equalto zero.

This law is also known as mesh rule or loop rule.

Sign Convention

Proper signs are to be assigned to EMFs and voltage drops acrossresistances in the closed circuit.

A rise in potential is considered positive and fall in potential is considerednegative.

VT

+V1- +V 2- +V3- +V N-

R1 R2 R 3 RN


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Example 11

In the circuit below, find vx and x.

5V

7V

100

+

vx

_

x

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Example 12

In the circuit below, find vx and x.

3V

1V

10

+

vx

_

x

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Example 13

In the circuit below, find vx .

60V8

10

4

2

5A+

vx

_

+

x

_

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Example 14

In the circuit below, find vx .

30V8

10

2

2

2A+

vx

_

+

x

_

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Example 16

Find all the branch currents and the voltage drops across variousresistors in the circuit shown below using Kirchhoffs Laws.

5V

10

25

10

15 10V

20V1


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Single Loop Circuit Page 37

120V30V

15

30

- is a circuit network with only one loop.

Example 17Compute the power absorbed by each element.


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Example 18

Compute the power absorbed in each element for the circuit shown below.

120V

30 2v A

+

-v A15

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Find the power absorbed by each of the five elements in the circuit below.

Example 19


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Example 20

Find the voltage v .

10

10

2

2

4 4A3A

+

v

_

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Calculate the power and voltage of the dependent source.

Example 21

15

6 6

4A9 3 6A 0.9i 3

i3

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Practice Question 1


0.25 v X

8V

+

-

20V

+

-8A

20V

+

-

- 12V +

- -v X +5A

2A

8V

+

-

7A

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Find the power absorbed by each of the five elements in the circuit below.

+

v x

_

30

12V

7

8

4v x

Practice Question 2


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Practice Question 3

unit 2 voltage and current sources

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