  # Current and Resistance Current flow through a metal. (Note: The electrons are colored differently to make tracking easier.) Current flow through a vacuum. (Note: The electrons are colored differently to make tracking easier.)

Q: "    A 9.0 volt battery is connected across a light bulb (R = 3.0 )
a. How many electrons pass through the resistor in one minute?
b. How many joules of energy are generated in one minute?"

A:
a
.  The resistance, R, of a conductor is the voltage, V, applied across the conductor divided by the current, I, through the conductor:

R = V / I .

Current, I, is the time rate of flow of charge, Q, through an area:

I = Q / t.

The amount of charge, Q, is simply a number of particles, z, multiplied by the charge per particle, q:

( Q = z q)

Using these facts we can derive and equation for the number of particles, z, passing through a conductor with resistance, R, in an amount of time, t:

R = V / I      ->     I = V / R =

I = V / R = Q / t  = ( z q ) / ( t )  =  V / R       ->

z = ( V * t ) / (R * q)

Now that we have a formula we can solve the problem.
V = 9.0 V
t = 1 minute = 60 s
R = 3.0 q = the charge of an electron = 1.60217733 x 10-19 C / electron

Solve for z:

z  = ( 9.0 V * 60 sec) / (3.0 * -1.6021917 x 10^-19 C / electron)
= 1.123 x 1022 (V sec)/ ( C / electron)
= 1.123 x 1022 ( (J/C) sec) / ( (J sec/C2) C / electron)
= 1.123 x 1022 ( J sec / C) / ( (J sec/ C) / electron)
= 1.123 x 1022 electrons

1.123 x 1022 electrons pass through the resistor in one minute.

b.  The power, P, loss in a conductor is the square of the current, I 2,   multiplied by the resistance, R:

P = I 2 R.

Using the fact that I = V / R we can rewrite this as:

P = V 2 / R .

Power, P, is energy, E, divided by time, t:

(P = E / t ).

Rewrite the equations:

P = V 2 / R as  E / t = V 2 / R.

This yields

E = V 2 t / R.

Now we can find the energy lost through the light bulb.

E  = V 2 t / R
= ( 9.0 V)2 * 60 sec / 3.0 = 4860 V2 sec / 3.0 = 1620 V2 sec / = 1620 ((J/C)2 sec) / ( J sec/C2)
= 1620 (J2 sec / C2) / (J sec/C2)
= 1620 J

The energy dissipated by the light bulb in 1 minute is 1620 Joules.

Q:     Do all conductors obey Ohm's Law?

A:    Yes, conductors are also called "Ohmic materials."

Q:     Two light bulbs use the standard 110 V light socket.  One is rated at 60 Watts and the other at 100 Watts.
a)  Which bulb carries the greater current?
b)  Which bulb has a higher resistance?
c)  Which bulb is brighter?

A:    The formula for power is P = I * V = (V/R) * V = V^2/R.
a)  Power is proportional to current, therefore the bulb with higher power carries greater current.
b)  Power is inversely proportional to resistance, therefore the bulb with lower power has a higher resistance. c)  Brightness is synonymous with intensity, I, and intensity is defined as "the portion of the power emitted by a point source, that reaches a unit area at a distance r from the source."  The total power of the source is uniformly spread over the area of sphere with radius r.   This is the very important and very well known law usually referred to in physics as "the one over r squared law."  It results that the bulb with higher power also provides higher intensity (or brightness) at a distance from it.

## References

### Definitions

Semiconductors: materials with few conduction electrons but with available conduction-level states that are close, in energy to their valance bands.  These materials become conductors when they are doped with other atoms that contribute electrons to the conduction band.

Superconductors: materials that lose all electrical resistance at low temperatures.

### Facts

The SI unit of electric current is the ampere (A):   1 A = 1 C/s.
The SI unit of resistivity is the ohm-meter ( m).

Ohm's Law:  for many materials (including most metals), the ratio of the current density to the electric field is a constant, , that is independent of the electric field producing the current.

### Equations

 Electric current (i) Current density (J) Drift speed of the charge carriers Resistance of a conductor R = V / i Resistivity ( ) and conductivity ( ) Ohm's Law J = E Resistance of a conductive wire of length L and uniform cross section Change of resistivity ( ) with temperature - 0 = 0 (T - T0) Resistivity of metals Power (rate of energy transfer) P = iV Resistive dissipation Color Code For Resistors Number Multiplier Tolerance (%) Black 0 1 Brown 1 101 Red 2 102 Orange 3 103 Yellow 4 104 Green 5 105 Blue 6 106 Violet 7 107 Gray 8 108 White 9 109 Gold 10-1 5% Silver 10-2 10% Colorless 20%

# List of Topics

 Measurements Electric Potential Magnetism Electrical Circuits (AC) Optical Instruments: Mirrors and Lenses Electrostatics Capacitance Sources of Magnetic Fields Maxwell's Equations Interference Electric Fields Current and Resistance Magnetism in Matter Electromagnetic Waves Diffraction Electric Flux Electrical Circuits (DC) Electromagnetic Induction Interaction of Radiation with Matter: Reflection, Refraction, Polarization  ครั้งที่

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