1. Mass training of trainers General Physics 2
May 23-25, 2017
Circuits & Kirchhoff’s Rule
Prof. MARLON FLORES SACEDON
Physics Instructor
Visayas State University
Baybay City, Leyte

2. How important is ELECTRICITY?

3. Electric Current What is an electric current?
An electric current is a flow of electric charge. In electric circuits this charge is often carried by moving electrons in a wire. It can also be carried by ions in an electrolyte, or by both ions and electrons such as in a plasma.
𝐼= 𝑄 𝑡
where Q is the electric charge transferred through the surface over a time t. If Q and t are measured in coulombs and seconds respectively, I is in amperes.
Andre Marie Ampere
Unit:
𝐼 → 𝑐𝑜𝑢𝑙𝑜𝑚𝑏 𝑠𝑒𝑐𝑜𝑛𝑑 = 𝐶 𝑠 = 𝑎𝑚𝑝= 𝐴

4. Two kinds of electric current?
Direct current (DC) is the unidirectional flow of electric charge. Direct current is produced by sources such as batteries, thermocouples, solar cells, and commutator-type electric machines of the dynamo type. Direct current may flow in a conductor such as a wire, but can also flow through semiconductors, insulators, or even through a vacuum as in electron or ion beams. The electric charge flows in a constant direction, distinguishing it from alternating current (AC). A term formerly used for direct current was galvanic current.
Alternating current (AC, also ac), the movement of electric charge periodically reverses direction. In direct current (DC, also dc), the flow of electric charge is only in one direction.
AC is the form of electric power delivered to businesses and residences. The usual waveform of an AC power circuit is a sine wave. Certain applications use different waveforms, such as triangular or square waves. Audio and radio signals carried on electrical wires are also examples of alternating current. An important goal in these applications is recovery of information encoded (or modulated) onto the AC signal.

5. Electric Current

6. Resistivity What is Resistivity (𝜌) of material?
a measure of the resisting power of a specified material to the flow of an electric current.
ratio between electric field 𝐸 and current density 𝐽 .
Unit: [Ω• m]

7. Resistivity
Temperature dependence of resistivity

8. Resistor
A device having a designed resistance to the passage of an electric current.
But:
The temperature dependence resistor

9. RESISTOR

10. Example
The 18-gauge copper wire has a cross-sectional area of 8.20x10-7.m2 It carries a current of 1.67 A. Find,
the electric-field magnitude in the wire;
the potential difference between two points in the wire 50.0 m apart;
the resistance of a 50m length of this wire.
Suppose the resistance of a copper wire is 1.05Ω at 200C , find the resistance at 00C and 1000C.

11. Example
The 18-gauge copper wire has a cross-sectional area of 8.20x10-7.m2 It carries a current of 1.67 A. Find,
the electric-field magnitude in the wire;
the potential difference between two points in the wire 50.0 m apart;
the resistance of a 50m length of this wire.
Suppose the resistance of a copper wire is 1.05Ω at 200 , find the resistance at 00C and 1000C.

12. Example
The 18-gauge copper wire has a cross-sectional area of 8.20x10-7.m2 It carries a current of 1.67 A. Find,
the electric-field magnitude in the wire;
the potential difference between two points in the wire 50.0 m apart;
the resistance of a 50m length of this wire.
Suppose the resistance of a copper wire is 1.05Ω at 200C, find the resistance at 00C and 1000C. a) b) c) or d)

13. Electromotive force
Electromotive force (emf) or (𝜀)

14. Electromotive force
Electromotive force (emf) or (𝜀)

15. Electromotive force
Figure shows a source (a battery) with emf 𝜀=12𝑉 and internal resistance 𝑟=2Ω . (For comparison, the internal resistance of a commercial 12V lead storage battery is only a few thousandths of an ohm.) The wires to the left of a and to the right of the ammeter A are not connected to anything. Determine the respective readings 𝑉𝑎𝑏 and I of the idealized voltmeter 𝑉 and the idealized ammeter 𝐴.
𝑉 𝑎𝑏 =?
𝐼=?
QUESTIONS

16. Electromotive force
Figure shows a source (a battery) with emf 𝜀=12𝑉 and internal resistance 𝑟=2Ω . (For comparison, the internal resistance of a commercial 12V lead storage battery is only a few thousandths of an ohm.) The wires to the left of a and to the right of the ammeter A are not connected to anything. Determine the respective readings 𝑉𝑎𝑏 and I of the idealized voltmeter 𝑉 and the idealized ammeter 𝐴.
𝑉 𝑎𝑏 =12𝑉
𝐼=0
ANSWER
No current passes through Ammeter

17. Electromotive force =2𝐴 =8𝑉 =8𝑉
Figure shows a source (a battery) with emf 𝜀=12𝑉 and internal resistance 𝑟=2Ω . (For comparison, the internal resistance of a commercial 12V lead storage battery is only a few thousandths of an ohm.) The wires to the left of a and to the right of the ammeter A are not connected to anything. Determine the respective readings 𝑉𝑎𝑏 and I of the idealized voltmeter 𝑉 and the idealized ammeter 𝐴.
= 12𝑉 4Ω+2Ω
𝐼= 𝜀 𝑅+𝑟
=2𝐴
By adding 4Ω resistor?
𝑉 𝑎 ′ 𝑏′ =𝐼𝑅
= 2𝐴 4Ω
=8𝑉 OR
𝑉 𝑎𝑏 =𝜀−𝐼𝑟
=12𝑉−(2𝐴)(2Ω)
=8𝑉

18. electric power in eLeCtriC CirCuits

19. Electric circuit
The flow of current

20. Electric Circuits What is an electric circuit?
An electric circuit is a path in which electrons from a voltage or current source flow. The point where those electrons enter an electrical circuit is called the "source" of electrons. 𝐼 𝐼 𝐼

21. Electric Circuits Two basic circuit connections Series connection +
𝑅 1
𝑅 2
𝑅 3
𝑉 𝑒𝑞
Parallel connection +
𝑅 1
𝑅 2
𝑅 3
𝑉 𝑒𝑞
𝑉 1
𝐼 1
𝐼 𝑇
𝑉 2
𝑉 2
𝑉 3
𝑉 1
𝐼 2
𝐼 1
𝐼 2
𝐼 3
𝐼 𝑇
𝑅 𝑒𝑞
𝑅 𝑒𝑞
𝐼 3
Formulas for simple parallel
𝑉 3
Formulas for simple series
1. Voltage is constant : 𝑉 𝑒𝑞 = 𝑉 1 = 𝑉 2 = 𝑉 3
1. Current is constant: 𝐼 𝑒𝑞 = 𝐼 1 = 𝐼 2 = 𝐼 3
Total current is the sum all point current:
𝐼 𝑒𝑞 = 𝐼 1 + 𝐼 2 + 𝐼 3
Total voltage is the sum all point voltages:
𝑉 𝑒𝑞 = 𝑉 1 + 𝑉 2 + 𝑉 3
3. Total resistance is the sum of reciprocal of all resistance :
1 𝑅 𝑒𝑞 = 1 𝑅 𝑅 𝑅 3
3. Total resistance is the sum of point resistance :
𝑅 𝑒𝑞 = 𝑅 1 + 𝑅 2 + 𝑅 3
For two resistance: 𝑅 𝑒𝑞 = 𝑅 1 𝑅 2 𝑅 1 + 𝑅 2

22. Electric Circuits
Formulas for simple series
1. Current is constant: 𝐼 𝑒𝑞 = 𝐼 1 = 𝐼 2 = 𝐼 3
Total voltage is the sum all point voltages:
𝑉 𝑒𝑞 = 𝑉 1 + 𝑉 2 + 𝑉 3
3. Total resistance is the sum of point resistance :
𝑅 𝑒𝑞 = 𝑅 1 + 𝑅 2 + 𝑅 3
Formulas for simple parallel
1. Voltage is constant : 𝑉 𝑒𝑞 = 𝑉 1 = 𝑉 2 = 𝑉 3
Total current is the sum all point current:
𝐼 𝑒𝑞 = 𝐼 1 + 𝐼 2 + 𝐼 3
3. Total resistance is the sum of reciprocal of all resistance :
1 𝑅 𝑒𝑞 = 1 𝑅 𝑅 𝑅 3
For two resistance: 𝑅 𝑒𝑞 = 𝑅 1 𝑅 2 𝑅 1 + 𝑅 2
Problem 1 Series connection: Calculate the following: Currents 𝐼 1 , 𝐼 2 , and 𝐼 3 and Voltages 𝑉 1 , 𝑉 2 , and 𝑉 3 .
Problem 2 Parallel connection: Calculate the following: Currents 𝐼 1 , 𝐼 2 , 𝐼 3 and 𝐼 𝑒𝑞 . And Voltages 𝑉 1 , 𝑉 2 , and 𝑉 3 . +
𝑅 1 =8Ω
𝑅 2 =10Ω
𝑅 3 =6Ω
𝑉 𝑒𝑞 =12𝑉 +
𝑉 𝑒𝑞=12𝑉
𝑅 1 =8Ω
𝑅 2 =10Ω
𝑅 3 =6Ω

23. Electric Circuits
Complex circuit
𝐼 𝑒𝑞 = 18𝑉 6Ω =3𝐴

24. Electric Circuits
Problem 3 Composite connection: Calculate the following: Currents 𝐼 1 and 𝐼 2 .
𝑅 4 =11Ω
𝑅 5 =5Ω
𝑅 6 =3Ω
𝑉 𝑒𝑞 =24𝑉 +
𝑅 1 =8Ω
𝑅 3 =10Ω
𝑅 2 =9Ω
𝐼 2
𝐼 1

25. Electric Circuits 𝑅 2 =9Ω 𝑅 4 =11Ω
𝑅 5 =5Ω
𝑅 6 =3Ω
𝑉 𝑒𝑞 =24𝑉 +
𝑅 1 =8Ω
𝑅 3 =10Ω
𝑅 2 =9Ω
𝐼 2
𝐼 1
Problem 3 Composite connection: Calculate the following: Currents 𝐼 1 and 𝐼 2 .
𝑉 1 = 𝑉 𝑒𝑞 =24𝑉: parallel
𝑅 𝑎 =19Ω
𝑉 𝑒𝑞 =24𝑉 +
𝑅 1 =8Ω
𝑅 3 =10Ω
𝑅 2 =9Ω
𝐼 2
𝐼 1
𝐼 1 = 𝑉 1 𝑅 1 = 24𝑉 8Ω =3A
Parallel: 𝐼 2 = 𝐼 𝑒𝑞 − 𝐼 1 =4.55𝐴−3=1.55𝐴
𝑉 𝑒𝑞 =24𝑉 +
𝑅 1 =8Ω
𝑅 𝑏 =6.55Ω
𝑅 2 =9Ω
𝐼 2
𝐼 1
𝑉 𝑒𝑞 =24𝑉 +
𝑅 𝑒𝑞 =5.28Ω
𝑉 𝑒𝑞 =24𝑉 +
𝑅 1 =8Ω
𝑅 𝑐 =15.55Ω
𝐼 2
𝐼 1
𝐼 𝑒𝑞 = 𝑉 𝑒𝑞 𝑅 𝑒𝑞 = 24𝑉 5.28Ω =4.55A

26. Electric Circuits Calculate the following. 𝑉 1 =? 𝑉 2 =? 𝑉 3 =? 𝐼 1 =?
𝐼 2 =?
𝐼 3 =?
𝑅 1 =220Ω
𝑅 2 =220Ω
𝑅 3 =220Ω
𝐒𝐮𝐩𝐩𝐥𝐲: 𝟗𝑽
𝐿𝐸𝐷 2 𝑉=?
𝐿𝐸𝐷 3 𝑉=?
𝐼 𝑒𝑞 =?
𝐿𝐸𝐷 1 𝑉=?
𝐿𝐸𝐷 1 𝐼=?
𝐿𝐸𝐷 2 𝐼=?
𝐿𝐸𝐷 3 𝐼=?
𝐿𝐸𝐷 1 𝑅=130Ω
𝐿𝐸𝐷 2 𝑅=130Ω
𝐿𝐸𝐷 3 𝑅=130Ω

28. LED - Light Emitting Diode

29. Electric Circuits
SOLVE THIS…….

30. Electric Circuits
SOLVE THIS……. 1
Figure

31. Kirchhoff’s Rule
Kirchhoff's circuit laws are two equalities that deal with the current and potential difference (commonly known as voltage) in the lumped element model of electrical circuits. They were first described in 1845 by German physicist Gustav Kirchhoff.[1] This generalized the work of Georg Ohm and preceded the work of Maxwell. Widely used in electrical engineering, they are also called Kirchhoff's rules or simply Kirchhoff's laws.
Gustav Robert Kirchhoff

32. Kirchhoff’s Rule
First, here are two terms that we will use often. The “JUNCTION and LOOP”.
A junction in a circuit is a point where three or more conductors meet.
A loop is any closed conducting path.

33. Kirchhoff’s Rule Where is the junction? a junction a junction
Not a junction
Not a junction
Where is the junction?
Not a junction
a junction
a junction
a junction
a junction

34. Kirchhoff’s Rule
loop3
Loop 1
Loop 2
loop3
Loop 1
Loop 2
Loop 3

35. Kirchhoff’s Rule Kirchhoff’s rules are the following two statements:
Kirchhoff’s junction rule: The algebraic sum of the currents into any junction is zero. That is,
Kirchhoff’s loop rule: The algebraic sum of the potential differences in any loop, including those associated with emfs and those of resistive elements, must equal zero. That is,

36. Kirchhoff’s Rule
Kirchhoff’s junction rule states that as much current flows into a junction as flows out of it.
The junction rule is based on conservation of electric charge. No charge
can accumulate at a junction, so the total charge entering the junction per unit
time must equal the total charge leaving per unit time

37. Kirchhoff’s Rule
Sign conventions when you apply Kirchhoff’s loop rule. In each part of the figure “Travel” is the direction that we imagine going around the loop, which is not necessarily the direction of the current.

38. Kirchhoff’s Rule
Problem 1: The batteries shown in the circuit in Figure have negligibly small internal resistances. Find the current through (a) the 30Ω resistor: (b) the 20Ω resistor; (c) the 10𝑉 battery.
Figure
At loop 1:
Σ𝑉=10− 𝐼 1 (30)=0
Loop 2
𝐼 1
𝐼 2
𝐼 1 =0.33𝐴
Loop 1
𝐼 3
At loop 2:
Σ𝑉=10− 𝐼 −5=0
𝐼 2 =0.25𝐴
At upper junction:
Σ𝐼= +𝐼 3 − 𝐼 1 − 𝐼 2 =0
+𝐼 3 −0.33−0.25=0
𝐼 3 =0.58𝐴

39. Kirchhoff’s Rule
EXAMPLE: The circuit shown in Figure below contains two batteries, each with an emf and an internal resistance, and two resistors. Find (a) the current in the circuit, (b) the potential difference Vab and (c) the power output of the emf of each battery.

40. Problem
Assignment 1

41. eNd