factors upon which resistance depends

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Resistance

                          All About Electric Resistance

At this page, we have a tendency to fully outline resistance & every important data regarding resistance

INDEX

• resistance or resistance is a constant term
• factors upon which resistance depends
• resistivity
• temperature coefficient of resistance 
• combination of resistance (SCR&PCR)                                          

RESISTANCE

Electric Resistance is a property of a resistor to oppose the flow of electric current through it.
OR
The flow of free electrons is called current, and resistance is the obstruction in the path of flow of electron.

NOTE: Conductors (metals) have very little resistance while insulators (glass rubber, mica, etc.) have a large amount of resistance.

Resistance is a constant term, that present where the flow of charge takes place

Mathematically,

V ∝ I
On removing proportionality sign (as a constant resistance comes),

V = IR

Where, 
v= volt, 
I= current, 
R= resistance (as a constant term)

Resistance can be denoted by (R or r)

The SI unit of resistance is ohm ( Ω).

If the potential difference (V) is 1 volt and current (I) is 1 ampere, then the Resistance (R) is 1 ohm

Resistance can be found by the "BBROYGBVGW" method.

Very high resistance is measured in mega-ohm and very low resistance in micro-ohm.

S.No.	Prefix	Symbol	Value in ohm (℧)
1.	Micro i.e. one millionth		10-6
2.	Milli i.e. one thousandth		10-3
3.	Kilo i.e. one thousand		103
4.	Mega i.e. one million		106

Factors upon which resistance depends:

• Length: The resistance R of a conductor is directly proportional to its length i.e. R directly proportional L                                               

R ∝ L

i.e., an increase in the length of a conductor increases its resistance and vice versa.  

• Area of cross-section: The resistance R of a uniform conductor is inversely proportional to its area of cross-section (A),                           

i.e., if we increase the cross-sectional area (A) of the conductor, it's resistance decreases and vice-versa. 

• Nature of material: The resistance of a material conductor also depends on the nature of its material. In a simple word, a material having a large number of free electron, lesser is the electric resistance.

For e.g. the resistance of nichrome wire is 60 times that of copper wire and of equal length of the cross-section area.

• Changes with temperature: i.e., resistance increase with the increase in temperature  

Neglecting the effect of temperature, for the time being, the electrical resistance of a conductor

  by combining both equations (1)&(2)

Where rho (ρ) is a constant and known as electrical resistivity or specific resistance of a conductor.

Resistivity:

The electrical resistivity of the material of a conductor is defined as the resistance of unit length and the unit cross-section area of the conductor.

                                               

The SI unit of resistivity is Ohm.    
              

Electrical resistivity depends on the nature of material and relaxation time.

Effect of temperature on resistance:

The effect of temperature on resistance depends upon the type of material

• The resistance increases with increase in temperature (for metals)
• 
  
• The resistance increase rise in temperature but he increases is very small or irregular (for alloy)
• 
  
• The resistance of semiconductors (Ge & Si), insulators (.e.g., glass, paper, mica, etc) and electrolytes decrease with an increase in temperature
• 
  

Temperature coefficient of Resistance:

·         

       suppose at 0 degree Celsius resistance is R_o

·         At 't' deg. C resistance increase to R_t

·         So increment in resistance is:
                                                                                       R_t - R_o

This increment in resistance depends on

·       
            Initial resistance of conductor (R_o)

·         R_t - R_o ∝ R_o

·         (R_t - R_o) ∝ t

·         On the nature of the material

So (R_t - R_o) ∝ R_ot  
  here, ∝ sign denotes proportional

On removing proportionality sign, a constant come (∝)

(R_t - R_o) = ∝R_ot

                      here, ∝ (alpha) is temperature co-efficient of resistance

  

                        here, Rt  is the value of resistance at any to temperature  

                        now, alpha (temperature of constant of resistance) is:

Combination of Resistance

There are two types of combination of Resistance

• ·         Series combination of Resistance
• ·         Parallel combination of Resistance

• Series combination of Resistance

·       

  
          -Current through each resistor is the same

·       

        -Sum of potential difference across individual Resistor is equal to the       potential difference applied by source,                                                 

V = V₁+V₂+V₃

·    
            -Equivalent Resistance,            

         R = R₁+R₂+R₃               ... (1)

·       
             -By Ohm’s law              

V₁ = IR₁                     V₂ = IR₂                      V₃ = IR₃

 Total potential difference (V) between A&B

From equation (1) we know that, R= R1+R2+R3

Therefore, 

• Parallel combination of Resistance:

·      

 -Voltage through each resistor is the same

·        
     -Sum of electric current flowing through the individual resistor is equal to   electric current drawn by the source,                       

I=I₁+I₂+I₃ 

·          
      -Equivalent Resistor,                 

       -By Ohm’s law,      

So, the total current:

We know that, 

Therefore,                                                  

Series and Parallel combination of Resistance

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