Electric Current

Current

• Rate at which charge flows through a surface.

I



dQ dt

Units - Ampere (A) • Ex. If the charge on a capacitor changes by the function

Q(t)=6(1-e

-

0.1t

)

, what is the charge on the capacitor and current leaving the capacitor at t = 5s?

Drift Velocity

• Factors that affect current flow

I

 

Q



t



nqv d A

n – carriers/volume q – charge/carrier A·v d = A  L/  t– volume/time • n depends on density of material and number of free electrons/atom.

• In a typical conductor drift velocity is ~0.25 mm/s. How does electrical devices respond so quickly?

Ohm’s Law

• Current Density is the amount of current per unit area.

J



I A



nqv d A

e e e e • Ohm’s Law The ratio of current density e e and electric field are constant.

J

   

E

Battery  - conductivity 12 V I Resistor 250 W

Resistance

• The common form of Ohm’s law is

V



I



R

• Resistance must then be related to length,  area, and conductivity.

R



l



A

 

l A

Units - Ohm’s ( W )  1   - resistivity  Temperature Dependence   0 ( 1   (

T

-

T

0 )) T 0 = 20 °C

Resistors

• Ex. What is the resistance of a cylindrical rod of carbon that is 2.0 cm long and has a radius of 0.50 mm? If 25 volts is applied across this resistor, how much current will flow?



carbon

 3 .

5  10 5 W 

m

What is the resistance at 40 °C?



carbon

 0 .

5  10 3 

C

1

Color Code

• Resistors have four color bands setting its value.

Color Black Brown Red Orange Yellow Green Blue Violet Gray White Value 0 1 2 3 4 5 6 7 8 9 1st 2nd × 10 Tolerance Value Gold 5% Silver None 10% 20% 3rd ± tolerance Ex. What is the value of the resistor?

Power

• Power is energy used per time.

P



U t



qV t



I



V P



I

2 

R



V

2

R

• How much power is used by a 0.89 W resistor when 25 volts is applied over it?

Defibrillator

• From the diagram can the current, voltage, resistance and power be calculated?

Semiconductors

• • Silicon and Germanium have 4 valence electrons and form 4 covalent bonds with its neighbors giving a neutral crystal structure.

Doping

– Using atoms with a valence of 3 or 5 give a deficit or surplus of electrons in the crystal structure.

P-type (missing e ) Un-doped N-type (extra e ) Si Si Si B Si Si Si Si Si 

<0.1

W

m

Si Si Si Si Si Si Si Si Si 

=23

W

m

Si Si Si P Si Si Si Si Si 

<0.1

W

m

P-type

PN Junctions

• Near the junction excess e- from N-type diffuse to places of missing e- in P-type semiconductors.

E field Diode N-type P-type Depletion Zone N-type P-type Depletion Zone N-type P-type N-type