2. Current and Resistance
The current is defined by the net charge flowing across the area A per unit time.
Thus if a net charge ΔQ flow across a certain area in time interval Δt,the average current Iav across this area is
التيار الكهربائي عدد الشحنات التي تعبر مساحة مقطع السلك في وحدة الزمن
In general the current I is
Current is a scalar quantity and has a unit of C/t, which is called ampere.

3. Drift velocity
The electric field produces electric force (F=qE) ,this force leads the free charge in the conductor to move in one direction with an average velocity .
المجال الكهربائي ينتج قوة كهربائية وهذة القوة تؤدي الى حركة الشحنات في الموصل وتتحرك في اتجاة واحد تعرف بسرعة الأنجراف

4. Definition of current in terms of the drift velocity
Suppose there are n positive charge particle per unit volume moves in the direction of the field from the left to the right, all move in drift velocity v. In time Δt each particle moves distance vΔt the shaded area in the figure, The volume of the shaded area in the figure is equal nAvΔt, the charge ΔQ flowing across the end of the cylinder in time Δt is  where q is the charge of each particle. Then the current I is
التيار الكهربائي=عدد الشحنات .شحنة كل شحنة.سرعة الأنجراف.المساحة g 

5. Definition of the current density
The current per unit cross-section area is called the current density J.

6. A copper conductor of square cross section 1 mm2 on aside carries aconstant current of 20 A .The density of free electrons is 8X1028 electron /m3
The current density is
J=I/A =20x106 A/m2
The drift velocity is
V=J/nq = 20x106 /(8X1028)(1.6X10-9) = m/s

7. Resistance and resistivity (Ohm’s Law
The current (I) passed through a conductor is directly proportional to voltage (V) across that conductor at constant temperature.
V  I
V = I R

8. Resistance
Degree of opposition that a material body opposes the passage of electric current. Ohm  Ohmmeter

9. The resistance in the circuit is drown using this symbol.
Fixed resistor Variable resistor Potential divider

10. Each material has different resistance therefore it is better to use the resistivity ,it is defined from
ρ =E/J
The resistivity has unit of Ω.m
The inverse of resistivity is known as the
conductivity σ
σ =1/ ρ

11. Evaluation of the resistance of a conductor
Consider a cylindrical conductor as shown in figure of cross-sectional area A and length l , carrying a current I. If a potential difference V is
connected to the ends the conductor, the electric field and the current density will have the values

12. The electrical resistance
It is defined as the opposition of the flow of electric current. Its SI unit is the ohm (Ω).
R = ρ L A
Where:
ρ is the resistivity of the material
L is the length
A is the cross sectional area

13. Resistivity ρ is electric field per density
ρ =E/J
The electrical conductivity
It is defined as the reciprocal of the resistivity. Its SI unit is (Ω -1 m-1)
σ = 1 / ρ

14. Example
A current of 4 mA flows through a bulb.How much charge enters the bulb in
1-One second
2-One minute
3-One hour.
1- Q = I t =(4x10-3) (1) = 4x10-3C
2- Q = I t =(4x10-3) (1x60) = 2.0x10-1C
3- Q = I t =(4x10-3) (1x60x60) = 20.0x10-1C

15. Example
If a conductor of length 20 m end cross-sectional area 1mm carries an electric current 20 mA,
Find:
1- Its resistance if you know that its resistivity is 5x10 -6 (Ω m )
2-Its conductivity
3-The potential difference across the conductor
1-R = ρ L = 5x (Ω m ) x =50(Ω )
A x 10 -6
2- σ = 1 / ρ = 1/ 5x = 0.2x 10 6(Ω -1 m-1)
3- V = I R = (20x ) (50) = 0.1 V

16. Electrical Energy and Power
If the positive terminal of the battery is connected to a and the negative terminal of the battery is connected to b of the device.
A charge dq moves through the device from a to b. The battery perform a work dW = dq Vab.
This work is by the battery is energy dU transferred to the device in time dt therefore,

17. Suppose a resistor replaces the electric device, the electric power is
The rate of electric energy (dU/dt) is an electric power (P).
Suppose a resistor replaces the electric device, the electric power is
The unit of power is (Joule/sec) which is known as watt (W )

18. Resistors in Series
The figure shows three resistor in series, carrying a current I.
For a series connection of resistors, the current is the same in each resistor

19. If VAD is the potential deference across the whole resistors, the electric energy supplied to the system per second is IVAD. This is equal to the electric energy dissipated per second in all the resistors.

20. The equivalent resistor is VAD = IR
The individual potential differences are
Therefore VAD = IR1The equivalent resistor is
The equivalent resistor is VAD = IR

21. Resistors in Parallel
The figure shows three resistor in parallel, between the points A and B,
A current I enter from point A and leave from point B, setting up a potential
difference VAB.

22. The current branches into I1, I2, I3, through the three resistors and,
The current in each branch is given by
The equivalent resistance is

23. What are the physical facts for the series and parallel combination of resistors?
Potential difference is the same through all resistors
Current is the same through all resistors
Total current=sum of the individual current
Total current=sum of the individual potential difference
Individual current inversely proportional to the individual resistance
Individual potential difference directly proportional to the individual resistance
Total resistance is less than least individual resistance
Total resistance is greater than greatest individual resistance