Physics 223

27. Current and Resistance

27.1 Electric Current

27.2 Resistance

27.3 A Model for Electrical Conduction

27.4 Resistance and Temperature

27.5 Superconductors

27.6 Electrical Power

27.1 Electric Current

current = charge / time

I = Q / t

I = dQ/dt

amps = coulombs/s

1A = 1 C/s

Electric Current

I = n q vd A

Current Density

J = I / A

J = n q vd

Ohm’s Law

Current Density depends on the electric field and the conductivity

J = E

Ohm’s Law … continued!

J = E

J = V/L

I = A V/ L

V = I (L/ A)

V = I R

Resistance

R = L/ A

Resistivity

The resistance of a wire depends on three factors

R = L / A

Resistance = Resistivity x Length / area

Example 27.1 . . . Hair dryer

A sticker on a hair dryer reads 120 V 10 A. The resistance of the heating element is most nearly

A. 0.12 B. 1.02 C. 12 D. 1200

Solution 27.1 . . . Hair dryer

Ohm’s Law says: volts = amps x ohmsV = I R120 = 10 x RR = 12 (say 12 ohms)

C. 12

Problem 27.2 . . . who's counting the electrons?

The number of electrons flowing per second through the heating element of the hair dryer is

A. 1.2 x 102

B. 1.6 x 10-19

C. 6.2 x 1027

D. 6.2 x 1019

Solution 27.2 . . . who's counting the electrons?

I = Q /tQ = 10 x 1Q = 10 CoulombsCharge of an electron is 1.6 x 10-19 Celectrons = 10 / 1.6 x 10-19

electrons = 6.2 x 1019

D. 6.2 x 1019

Problem 27.3 . . . All about

Two wires are made of the same material. Wire 1 is twice as long as wire 2 but is thinner and has half the radius of wire 2.

A. R1 = R2 and 1 = 2

B. R1 = 2R2 and 1 = 2

C. R1 = 4R2 and 1 = 2 2

D. R1 = 8R2 and 1 = 2

Solution 27.3 . . . All about

The cross-sectional area varies as the square of the radius. So the cross-sectional area of wire 1 is a quarter of the cross-sectional area of wire 2. This factor by itself would make the resistance of wire 1 four times that of wire 2. In addition, wire 1 is twice as long which would make its resistance twice as much. All told R1 = 8R2. Note that the wires are made of the same material so 1 = 2. The correct choice is D.

27.4 Resistance and Temperature

= 0 [ 1+ ( T – T0 )]

R = R0 [ 1+ ( T – T0 )]

is coefficient of resistivity

27.5 Superconductors

Below a critical temperature resistance decreases to ZERO!

27.6 Electrical Power

W = Q V

P = W / t

P = V Q /t

P = V I

Example 27.4 . . . Hair dryer

A sticker on a hair dryer reads 120 V 10 A. The power rating is

A. 12 WB. 120 WC. 1200 WD. 12000 W

Solution 27.4 . . . Hair dryer

C. 1200 W

That’s all folks!