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3.1.6.       Electric Current & Resistance <CJ chap  20.1-20.7 >

3.1.6.1. Discussion

3.1.6.1.1.     Electrical current is defined as the amount of charge in Coulombs that flows per second past a point

3.1.6.1.1.1. The unit of electrical current is the Ampere = Coulomb / Second  or A =C/s

3.1.6.1.1.2. Electrical current flows because of a potential difference between two points in a material

3.1.6.1.2.     There is resistance to all flow of electrical current except in superconductors.

3.1.6.1.2.1. One finds that the ratio of the voltage,  to the current that flows, is a constant called the resistance

3.1.6.1.2.2. Electrical resistance is measured in Ohms = Volts / Ampere   W = V/A

3.1.6.2. Mathematical

3.1.6.2.1.     Electric current = I = D Q / D t   <Ampere (A)  = Coulomb / second>

3.1.6.2.2.     Ohm’s law:      R = V/I  <Ohm = Volt / Ampere>   is generally constant thus  V = IR 

3.1.6.2.3.     Resistors in series & parallel:

3.1.6.2.3.1. Resistors in series:   R_series = R₁ + R₂ + R₃ + …

3.1.6.2.3.2. Resistors in parallel:   1/R_parallel = 1/R₁ + 1/R₂ + 1/R₃ + …

3.1.6.2.4.     Resistively  r:       R = r l / A  where  r is defined for a given material

3.1.6.2.4.1. r_silver = 1.59E-8   r_copper = 1.72E-8     r_aluminum = 2.82E-8   r_iron = 9.7E-8

3.1.6.2.4.2. r_carbon = 3.5E-5                           r_wood = 3E10     r_glass = 10¹⁰ to 10¹⁴   

3.1.6.2.4.3. r depends upon temperature:   r =  r₀ (1 + a (T-T₀) )

3.1.6.2.4.4. s = 1/r  = electrical conductivity of a substance

3.1.6.2.5.     Power Loss  P = IV  = I²R

3.1.6.3. Advanced

3.1.6.3.1.     Electric current I = dQ/dt  

3.1.6.3.2.     Electric current density   j =  v dq/ dA             << check these equations ***

3.1.6.3.3.     Ohms law with current density   j = s E