Electric Circuit Elements and Power Calculation, Lecture notes of Electronics

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Module 02

Electric Circuit Elements, Voltage & Current Sources, Resistors, Ohm’s

Law, Kirchhoff's Law, Voltage Division, Current Division, Delta-Wye

Transformation

Electric Circuit Elements

1) Ideal (Independent) Sources

 Delivers a prescribed voltage independent of the current flowing.

v

i

i-V Characteristics

Ideal Voltage Source

2) Controlled (Dependent) Sources

 The voltage or current of the source depends on another voltage or current

elsewhere in the circuit.

Type of Sources in Circuits

A. Constant Sources

B. Sinusoidal Sources

 D irect C urrent ( DC ) Signals

 Normally represent signal from battery

 DC Power Supply Sources

 A lternating C urrent ( AC ) Signals

 Sine waveform

 Normally represent signal from power outlet

 Function generator

5) Conductance

 Is the reciprocal of resistance.

ܩ =

1

ܴ

 Units: siemens (S)

Review

If the interconnection is valid, find the total power developed by the

voltage sources. If the interconnection is not valid, explain why?

௟௢௢௣

Thus, interconnection is not valid

Solution

Solution

KVL around mesh 1 (CW):

− 50 − 20 ݅ (^) ఙ + 18 ݅ (^) ∆ = 0

KVL around mesh 2 (CW):

− 18 ݅ (^) ∆ + 5 ݅ (^) ఙ + 40 ݅ (^) ఙ = 0

Solve:

− 50 − 20 ݅ (^) ఙ + 5 ݅ (^) ఙ + 40 ݅ (^) ఙ = 0

݅ ఙ = ܣ

Sub ݅ ఙ = ܣ2:

(a)

Thus : ݒ଴ = 2A 40 Ω = ૡ૙ ܄

Solution

(b)

at node A: ݅ ௫ = ݅∆ + ݅௬

A B

݅ ∆ = 5A

ܲ ௗ௘௟௜௩௘௥௘ௗ (" − " sign): ܲ =^ ݅ݒ

To find ݅ ௫, apply KCL :

෍ ݅௜௡ = ෍ ݅௢௨௧

at node B: ݅ ௬ = ݅ఙ + ݅8 (^) ∆

Solve: ݅ ௫ = 47 ܣ, ݅௬ = 42 ܣ

= − 2350 W

= − 1880 W

ܲ ௔௕௦௢௥௕௘ௗ = (݅ ∆)ଶ^18 + (݅ ఙ)ଶ^40 + 5 ݅ ఙ ݅௬ + ݒ௫ 8 ݅ ∆ + 20 (݅8 ∆)

ܲ ௔௕௦௢௥௕௘ௗ (" + " sign): (^) ܲ = ݅ ଶܴ

To find ݒ௫, apply KVL :

෍ ݒ = 0 ௟௢௢௣ −ݒ଴ + ݒ௫ + 20 = 0 ݒ௫ = ݒ଴ − 20 = 80 − 20 = 60 ܸ

∴ ෍ ࡼࢊࢋ࢘ࢋ࢜࢏࢒ࢋࢊ = ෍ ࡼࢊࢋ࢈࢘࢕࢙࢈ࢇ = ૝૛૜૙ ࢃ

− 4230 W

Parallel Resistors & Current Division

 Parallel-connected circuit elements have the same voltage.

 Parallel elements are connected between the same nodes.

KCL from node a to node b:

݅ ௦ = ݅ଵ + ݅ଶ + ݅ଷ + ݅ସ

Ohm’s Law

௦ ܴ ଵ

௦ ܴ ଶ

௦ ܴ ଷ

௦ ܴ ସ

Thus, ܸ ௦ =

௦ 1 ܴ ଵ +^

ܴ ଶ +^

ܴ ଷ +^

Review

Find power delivered by the 5 A source?

Solution Simplified and find an equivalent circuit. Starts by combining elements from right to left.

௘௤ =^ ܴ ଺଴Ω//ܴ^ ଷ଴Ω =^

∴ ࡼ࡭૞= ܫଶ^ ܴ = (ܣ5)ଶ^20 Ω = ࢃ૞૙૙

Wheatstone Bridge

 The Wheatstone bridge circuit is used to precisely measure resistances.

 To find the value of ܴ ௑ , we adjust the variable resistor ܴ ଷ until there is no current in the galvanometer.

 Then calculate the unknown resistor using

ܴ ௑ =

ܴ ଶ ܴ ଵ

ܴ ଷ

Review

(a) Find resistance as seen by the voltage source?

(b) Find power dissipated in 31 Ω resistor.

Solving this will introduces the concepts of Wye & Delta circuits (Tee & Pi Circuits).

Answers

(a) ܴ ௘௤ = 80 Ω

(b) ܲ ଷଵΩ = ܹ