1. Current and Resistance
Chapter 2
Current and Resistance
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2. Objectives : Define the current.
Understand the microscopic description of current.
Discuss the rat at which the power transfer to a device in an electric current.
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3. 2- Current and Resistance (Ch 27 in serway)
2-1 Electric current
2-2 Resistance and Ohm’s Law
2-3 Current density, conductivity and resistivity
2-4 Electrical Energy and Power
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4. 2-1 Electric Current
Whenever electric charges of like signs move, an electric current is said to exist.
The current is the rate at which the charge flows through this surface
Look at the charges flowing perpendicularly to a surface of area A
The SI unit of current is
Ampere (A) 1 A = 1 C/s
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5. ∆Q is the amount of charge that passes through this area in a time interval ∆ t,
the average current Iav is equal to the charge that passes through A per unit time
We define the instantaneous current I as the differential limit of average current:
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6. Electric Current, cont
The direction of the current is the direction positive charge would flow
This is known as conventional current direction
In a common conductor, such as copper, the current is due to the motion of the negatively charged electrons
It is common to refer to a moving charge as a mobile charge carrier . A charge carrier can be positive or negative. For example, the mobile charge carriers in a metal are electrons.
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7. Current and Drift Speed
Charged particles move through a conductor of cross- sectional area A
n is the number of charge carriers per unit volume
n A Δx is the total number of charge carriers
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8. Current and Drift Speed, cont
The total charge is the number of carriers times the charge per carrier, q
ΔQ = (n A Δx) q
The drift speed, vd, is the speed at which the carriers move
vd = Δx/ Δt
Rewritten: ΔQ = (n A vd Δt) q
Finally, current, I = ΔQ/Δt = nqvdA OR
the average current in the
conductor
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9. Current and Drift Speed, final
If the conductor is isolated, the electrons undergo random motion
When an electric field is set up in the conductor, it creates an electric force on the electrons and hence a current
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10. Charge Carrier Motion in a Conductor:
The zig-zag black line represents the motion of charge carrier in a conductor
The net drift speed is small
The sharp changes in direction are due to collisions
The net motion of electrons is opposite the direction of the electric field
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11. 2-2 Resistance
Consider a conductor of cross-sectional area A carrying a current I. The current density J in the conductor is defined as the current per unit area. Because the current I = nqvdA,
the current density is:
the current density is proportional to the electric field:
Where σ the constant of proportionality & is called the conductivity of the conductor.
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12. and
If the field is assumed to be uniform, the potential difference is related to the field through the relationship
express the magnitude of the current density in the wire as
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13. Where ,J = I/A, we can write the potential difference as
The quantity R = ℓ/σA is called the resistance of the conductor. We can define the resistance as the ratio of the potential difference across a conductor to the current in the conductor:
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14. The resistance R of an element denotes its ability to resist the flow of electric current; it is measured in ohms. The resistance of any material is dictated by four factors:
1. Material property—each material will oppose the flow of current differently.
2. Length—the longer the length , the more is the probability of collisions and, hence, the larger the resistance.
3. Cross-sectional area—the larger the area A, the easier it becomes for electrons to flow and, hence, the lower the resistance.
4. Temperature—typically, for metals, as temperature increases, the resistance increases
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15. Thus, the resistance R of any material with a uniform cross- sectional area A and length (as shown in Fig) is directly proportional to the length and inversely proportional to its cross-sectional area. In mathematical form,
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17. Quiz 1: A cylindrical wire has a radius r and length L
Quiz 1: A cylindrical wire has a radius r and length L. If both r and L are doubled, the resistance of the wire, (a) increases (b) decreases (c) remains the same.
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18. SOLUTION: (b) decreases The doubling of the radius causes the area A to be four times as large, so tells us that the resistance decreases.
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19. Example 1:
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21. Resistance
In a conductor, the voltage applied across the ends of the conductor is proportional to the current through the conductor
The constant of proportionality is the resistance of the conductor
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22. Resistance, Units of resistance are ohms (Ω) 1 Ω = 1 V / A
Resistance in a circuit arises due to collisions between the electrons carrying the current with the fixed atoms inside the conductor
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23. 2-2 Ohm’s Law
Experiments show that for many materials, including most metals, the resistance remains constant over a wide range of applied voltages or currents
This statement has become known as Ohm’s Law
ΔV = I R
Ohm’s Law is an empirical relationship that is valid only for certain materials
Materials that obey Ohm’s Law are said to be Ohmic
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24. Ohm’s Law, cont An ohmic device
The resistance is constant over a wide range of voltages
The relationship between current and voltage is linear
The slope is related to the resistance
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25. Ohm’s Law, final
Non-Ohmic materials are those whose resistance changes with voltage or current
The current-voltage relationship is nonlinear
A diode is a common example of a non-Ohmic device
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26. Summary The electric current I in a conductor is defined as
The average current in a conductor is related to the motion of the charge carriers through the relationship
The magnitude of the current density J in a conductor is the current per unit area:
The current density in an ohmic conductor is proportional to the electric field according to the expression
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27. The resistance R of a conductor is defined as
where ∆V is the potential difference across it, and I is the current it carries.
For a uniform block of material of cross sectional area A and length L, the resistance over the length L is
where ρ is the resistivity of the material.
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