Nodes and branches and Kirchhoff's current laws

Nodes and branches and Kirchhoff's current laws along with their explanation and numericals

1. ELECTRONICS ICODE 308165LECTURE 3

2. EXAMPLE 1.5

3. THE KILOWATT HOUR (KWH)
§ElectricalsupplyauthoritiesusethekWhasthe
unitformeasuringelectricalenergyto
householders
§Electricalenergysuppliedtoconsumersisbought
bytheUNIT.TheUNITisthekilowatthour(kWh).
Onekilowatthouristheamountofenergythat
wouldbeconvertedbyaonethousandwatt
appliancewhenusedforonehour
§IkWh=3600KJ

4. EXAMPLE 1.6

5. PASSIVE SIGN CONVENTION
§Bythepassivesignconvention,powerispositivewhencurrent
entersthroughthepositivepolarityofthevoltage.Inthiscase,!=
#$or#$>0impliesthattheelementisabsorbingpower.
§However,if!=−#$or#$asinFig.1.8(b),theelementisreleasingorsupplyingpower.

6. EXAMPLE 1.7
§Calculate the power supplied or absorbed by each element
§We will follow passive sign convention

7. Short Circuit
§When R = 0
"=$%=0
Open Circuit
§When R=∞
Then $=0
Circuit Conventions
A short circuit is a circuit
element with resistance
approaching zero.
Anopencircuitisacircuit
elementwithresistance
approachinginfinity.

8. CHAPTER 1 ENDS
§Go through Summary & Review Questions at the end of Chapter 1.
§Solve Examples and problems 1.13 to 1.17 for practice

9. 2.2 OHM’S LAW
Riv
iRv
abab=
=
The voltage #across a resistor is directly proportional to the
current$flowing through the resistor

10. RESISTANCE
§Resistanceisthepropertyofthecircuitelementwhichoffer
hindranceoroppositiontotheflowofcurrentandintheprocess
electricenergyisconvertedintoheatenergy
§Aresistorisadevicethatprovidesresistanceinanelectriccircuit
§UnitofResistance(R)isohm(Ω);1Ω=1V/1A
-ρ:Resistivity,
-L=Lengthofconductor,
-A=AreaofConductor
A
L
R
r
=

11. RESISTANCE RELATED TO PHYSICAL PARAMETERS

12. RESISTIVITY OF VARIOUS MATERIALS AT ROOM TEMPERATURE (300 K)

13. OHM’S LAW
§Ohm’slawstatesthatthevoltagevacrossaresistorisdirectly
proportionaltothecurrentiflowingthroughtheresistorof
resistance((Ω).
#=$,
§Conductance:Conductanceisanexpressionoftheeasewith
whichelectriccurrentflowsthroughasubstance.Measuredinmho
(℧)orSiemens(S)
Gvi
R
G
=
=
1

14. POWER RATING OF RESISTANCE
!=#$
¡Ohm law states
#=$,
¡Substitute for #
!=$2,
¡Similarlywe substitute for $to get
!=#2/,
¡Thepowerratingisthemaximumallowablepowerdissipationin
theresistance.Exceedingthisratingleadstooverheatingand
cancausetheresistancetoburnup.

15. NODES AND BRANCHES
§Node–Ajunctionwhere2ormoreelementsconnectiscalled
anode.
§Branch–Branchesaretheconnectionsbetweennodes.Abranch
representsanytwo-terminalelement(resistor,capacitor,source,etc.).Thenumberofbranchesinacircuitisequaltothenumberof
elements.
§Loop–Aloopisanyclosedpathgoingthroughcircuitelements.

16. NODES AND BRANCHES

17. KIRCHHOFF’S CURRENT LAW
§Kirchhoff’s current law (KCL) states that the algebraic sum
of currents entering a node is zero.

18. KIRCHHOFF’S CURRENT LAW
§$1+$3+$4−$2−$5
§$1+$3+$4=$2+$5

19. KIRCHHOFF’S CURRENT LAW

20. KIRCHHOFF’S VOLTAGE LAW
§Kirchhoff’s voltage law (KVL) states that the algebraic sum
of all voltages around a closed path (or loop) is zero.

21. KIRCHHOFF’S VOLTAGE LAW
§−"1+"2+"3−"4+"5=0
§"2+"3+"5="1+"4

22. KIRCHHOFF'S VOLTAGE LAW

23. PROBLEM
§Find i1, i2 and i3.