Current Electricity 11th

Resistance. The electrical resistance of a circuit  device is defined as the ratio of the voltage applied to the electric current which flows through it: If the resistance is constant over a considerable range of voltage, then Ohm's law, 

                                       I = V/R, 

can be used to predict the behavior of the material.

Resistivity, commonly symbolized by the Greek letter rho, ρ, is quantitatively equal to the resistance R of a specimen such as a wire, multiplied by its cross-sectional area a, and divided by its length l; ρ = Ra/l.

Ohm's law in terms of Resistance R= V/I

Resistances in Series : 
                      

         V =V1 + V2 + V3

            IR = IR1 + IR2 +IR3

                  = I(R1 + R2 +R3)

             R  =   R1 + R2 + R3

Resistances in Parallel : 

         I = I1 + I2 

       V/Rp = V/R1 + V/R2

           V/Rp = V(1/R1 + 1/R2)

       1/Rp = 1/R1 + 1/R2

                   Rp = R1R2 / (R1 + R2)