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 v d A

Current Density J = I / A J = n q v d

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 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 Hair dryer Ohm’s Law says: volts = amps x ohms V = I R 120 = 10 x R R = 12  (say 12 ohms) C.12 

Problem 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 10 2 B.1.6 x C.6.2 x D.6.2 x 10 19

Solution who's counting the electrons? I = Q /t Q = 10 x 1 Q = 10 Coulombs Charge of an electron is 1.6 x C electrons = 10 / 1.6 x electrons = 6.2 x D.6.2 x 10 19

Problem 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.R 1 = R 2 and  1 =  2 B.R 1 = 2R 2 and  1 =  2 C.R 1 = 4R 2 and  1 = 2  2 D.R 1 = 8R 2 and  1 =  2

Solution 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 R 1 = 8R 2. 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 – T 0 )] R = R 0 [ 1+  ( T – T 0 )]  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 Hair dryer A sticker on a hair dryer reads 120 V 10 A. The power rating is A.12 W B.120 W C.1200 W D W

Solution Hair dryer C.1200 W

That’s all folks!