Physics 32N

8/9/2019 Physics 32N

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Current, Resistance and

Electromotive Force

Ms. ArlynM. Roque Chap 25 - Current, Resistanceand Electromotive Force

1






3

• The current I through the cross-sectional area A is the netcharge flowing through that areaper unit time.

• For a net charge dQ that flowsthrough an area in a time d t , thecurrent I through the area is

=

Definition of Current



Current and Direction of Flow


4

• The conventional current I is in the direction of the flow of positive

charges• SI unit is ampere; 1 A = 1 C/s

In both cases: Net flow of positive charges from left to right.




5

The total charge dQ that flows out theend of the cylinder during the time d t is

=

and the current is

=

= .

The current density is

=

= .

Current Density




6

Copper has 8.5 × 102 free electrons per cubic meter. A71.0-cm length of 12-gauge copper wire that is 2.05 mm indiameter carries 4.85 A of current.

(a) How much time does it take for an electron to travel thelength of the wire?

(b) Repeat part (a) for 6-gauge copper wire (diameter 4.12mm) of the same length that carries the same current.

(c) Generally speaking, how does changing the diameter ofa wire that carries a given amount of current affect the

drift velocity of the electrons in the wire?

Sample Exercise




7

The current in a wire varies with time according to therelationship = 55 A − 0.65 A/s 22.

(a) How many coulombs of charge pass a cross section of

the wire in the time interval between t = 0 and t = 8.0 s?(b) What constant current would transport the same charge

in the same time interval?

Sample Exercise




8

• The current density J in a conductor depends on the electric field E and on the properties of the material.

• For metals, J is directly proportional to E and the constant ofproportionality is the resistivity of the material

= , =

SI unit is Ω•m.

• Resistivity is an inherent property of the material which depends ontemperature:

= + ( − )

where α is the temp c oef of resis t iv i ty ( in K1).

• The reciprocal of resistivity is known as conduct iv i ty .

Resistivity




9

Since resistivity has units of ohm-meter , you might think that you can just divide by the length of a material to find its resistance in ohms.

since = / and = /

Resistivity is =

=

/

/ = /.

Resistance from resistivity is =

Dependence on temperature:

= + ( − )

?/ L R

Resistance




10

Three resistors are made of the same material, withsizes in mm shown below. Rank them in order of total

resistance, greatest first.

A. I, II, III.

B. I, III, II.C. II, III, I.

D. II, I, III.

E. III, II, I.

4

4

52

6

3

I.

II.

III.

Each has

square

cross-section

Check Your Understanding




11

A copper wire has a diameter of 1.02 mm and a cross-section area A = 8.2x10-7 m2. It carries a current I = 1.67 A.Find (a) the electric field magnitude in the wire; (b) thepotential difference between two points in the wire 50 mapart; (c) the resistance of a 50 m length of this wire.

Answer:

(a) E = J = I / A = 0.035 V/m. (b) V = EL = 1.7 V.

(c) R = V / I = L / A = 1.0 W.

Sample Exercise




12

A certain potential difference is placed across a solidcylindrical resistor. The current through the resistor is 2 A.

a. If the diameter of this resistor is doubled, what will be

the value of the current?

b. If the length of the resistor is increased by 25% from theoriginal, what is the new value of the current?

Answer:

a. I = 8 Ab. I = 1.6 A

Sample Exercise

EMF d Ci i



−

-

-

+

+

+


13

• For a conductor to have a steady current, it must be part of a paththat forms a closed loop or complete circuit.

−

-

-

+

+

+

=

=

=

↓

↑

EMF and Circuits

• Every complete circuit with a steady current must include emf s ource .

• The maximum potential difference bet. the terminals of such device is ε.

EMF d Ci it




14

• Every complete circuit with a steady current must include emf s ource .

• The maximum potential difference bet. the terminals of such device is ε.

EMF and Circuits

• Within the emf device, positive charge carriers move from a region oflow electric potential to a high electric potential.

EMF S




15

• In an ideal voltage source, emf is equal to the terminal voltage.

= =

EMF Source

• If a voltage source has an internal resistance :

= −

= =

+

E d P i El t i Ci it




16

• Power is the rate at which energy is either delivered to or extracted froma circuit element.

=

Energy and Power in Electric Circuits

• Power delivered to a resistor

= = =

• Power delivered from an emf source with internal resistance

= −

• Power delivered to an emf source with internal resistance

= +

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Physics 32N