Resistance.

Resistance

Resistance is that property of circuit element by virtue of it opposes the flow of current passing through it. The SI unit of electrical resistance is the ohm (Ω). Resistance of the material is depends upon different parameters of materials like whether it is conductor, insulator, or semiconductor, physical conditions and it also depends upon dimension of material of material.

Resistance of a Material

                  

R = pl/a

p = resistivity or specific resistance

l  = length of the conductor

a = area of cross-section    =   πr²

Resistivity or Specific Resistance

Resistivity is measure of circuit element’s ability to oppose the flow of current. Resistivity is the reciprocal of electrical conductivity

p   =   1/ơ

ơ  =  electrical conductivity

Resistor

A resistor is an electrical component which implements electrical resistance in a circuit. It is a passive element.

Resistor converts electrical energy into heat energy.

                 

P = VI = (IR)I = I²R

W = ₀∫^t I²R dt  =  I²Rt 

(⇒Heat dissipated in resistor)

Ohm’s Law

It States that at constant temperature potential difference across to an element is directly proportional to the current flow through it.

                  

             IαV

             I = V/R   I=GV

             1/R = G

R = Resistance

G= Conductance

V = IR

R = pl/A

V=Ipl/A

I/A=V/lp

J=pE

JαE

This is another form of ohms law and it states that at constant temperature current density is directly proportional to electric field intensity.

For ohms law to be valid the temperature and conductivity of material should be constant.

Practically we have seen that resistance of metallic conductor varies with temperature.

Rt₂ = Rt₂(1+α∆T)

 

Average power dissipated in resistor

 

Voltage and current across a resistor are in same phase.

Pₐ_v  =  1/T ₀∫^t v(t). i(t). dt

   ⇒  1/T ₀∫^t(V_m Sinwt) (I_m Sinwt) dt

   ⇒ V_mI_m/2 ₀∫^t (1- Cos2wt)dt

Pₐ_v   =  V_mI_m/2

        ⇒(V_m/√2). (I_m/√2)

P_av   ⇒V_rms. I_rms

 

Combination of Resistors

 

Series Combination of Resistors and Voltage Division

R_ab =  R₁ + R₂ + R₃          (Equivalent Resistance or Effective Resistance)

Voltage across R₁ = V₁

V₁ = (V_ab*R₁)/(R₁ + R₂ + R₃)

Similarly V₂ = (V_ab*R₂)/(R₁ + R₂ + R₃)

Similarly calculate  V₃

 

Parallel Combination of Resistor and Current Division

Methods of Resistance Measurement

 

Low Resistance

Resistor having resistance value R less than 1Ω is categorized as low resistance.

Examples Copper / Aluminium winding of motors, generators and transformers, earth conductor resistance

Low resistance is measured by using Kelvin Double Bridge and Potentiometer Method

 

Medium Resistance

Resistor having resistance value R greater then 1Ω and less then 100KΩ is categorized as medium resistance.

Examples electric heater, oven, iron box, electronic circuit etc.

Medium resistance is measured by using Wheat-stone Bridge, Carry Foster Slide Wire Bridge and ohmmeter method.

 

High Resistance

Resistor having resistance value R greater then 100KΩ  is categorized as high resistance.

Examples insulation resistance of cable, motor, generator, transformer etc.

High resistance is measured by using Mega-Ohm Bridge, Megger and Direct Deflection Method.

# Inductor