Chapter 28 Current and Resistance

第二十八章 電流及電阻

Moving charges

Electric currentThe current is the rate at which charge flows through this surface.

The direction of the current is defined to be the direction of the positive charge flow. However, in metals, electrons flow in the opposite direction of the current.

Definition and unit of currentdq

idt

The unit of current is called the ampere (A):

1 1 /A C s

Current is a scalar, even though we often use an arrow to indicate the current flow directions in wires.

0 2 2i i i i0

i2

i1

Sample problem 1Water flows through a garden hose at a volume flow rate of 450 cm3/s. What is the current of negative charge?

Ans: 2.42 107 A = 24.1 MA

Current density

i J dA

i J A

If the current density is uniform:

i JAIf the current density is also normal to the surface:

Drift speedq

it

dq enAv t di enAv

dJ nev

Sample problem 2(a)The current density in a cylindrical wire of radius R = 2.0 mm is

uniform across a cross section of the wire and is J = 2.0 105 A/m2. What is the current through the outer portion of the wire between radial distances R/2 and R?

(b)Suppose, instead, that the current density through a cross section varies with radial distance r as J = ar2, in which a = 3.0 1011 A/m4 and r is in meter. What is the current through the same outer portion of the wire?

(a) 1.9 A; (b) 7.1 A.

Sample problem 3What is the drift speed of the conduction electrons in a copper wire with radius r = 900 m when it has a uniform current i = 17 mA? Assume that each copper atom contributes one conduction electron to the current and the current density is uniform across the wire’s cross section.

Ans. vd = 4.9 10-7 m/s.

28 31( ) 8.49 10A massn N mM

d

ij nev

A

Resistance V

Ri

1 1 1 /ohm V A

Ohm’s law

Georg Simon Ohm (1789-1854)

V iR V El JAR

E J

J E

or

lR

A

I-V curves Ohm’s law

Color coding for resistors

Variation with temperature

0 0 0( )T T

where T0 is a selected reference temperature and ρ0 is the resistivity at that temperature. Usually T0 = 293 K, for which ρ0 = 1.69 10-8 ·m for copper.

Sample problem 4A rectangular block of iron has dimensions 1.2 cm 1.2 cm 15 cm. A potential difference is to be applied to the block between parallel sides and in such a way that those sides are equipotential surfaces. What is the resistance of the block if the two parallel sides are (1) the square ends, and (2) two rectangular sides.

A microscopic view

A microscopic view of Ohm’s law

idv qE

dt m

0i i

qEv v t

m

0 0i i i i

qEv v v v t

m

d iv v

0 0iv

t

d

qEv

m d

Jv

nq

2

mE J

nq

2

m

ne

2ne

m

Sample problem 5(a) What is the mean free time between collisions for the conduction electrons in copper? (b) What is the mean free path between collisions for the conduction electrons in copper, assuming that their effective speed veff is 1.6 106 m/s?

(a) 142

2.5 10m

sne

(b) 84.0 10 40effv m nm

Power in electric circuits

( ) ( )dU dq V idt V

/P dU dt iV

2 2 /P iV i R V R

Sample problem 6A length of heating wire, made of nickel-chromium-iron alloy called Nichrome, has a resistance R of 72 . At what rate is the energy dissipated in each of the following cases? (1) A potential difference of 120 V is applied across the full length of the wire. (2) The wire is cut in half, and a potential difference of 120 V is applied across the length of each half.

semiconductors

superconductors

Levitation with superconductors

Home work

Question ( 問題 ): 12, 15, 16

Exercise ( 練習題 ): 5, 11, 15

Problem ( 習題 ): 14, 38, 40, 42