Conductor | Insulator | Combination of Resistors

CONDUCTORS

  Why do we always use metal wire for conduction of electricity?

Conductor: Because, they are good conductor of electricity and offer less resistance to the flow of current. But how can they conduct with much ease? Metal like silver and copper have overabundance of free electrons which are not held firmly with a particulars of metal. These free electrons moves randomly in all direction insides of metals When we apply external electric field these electrons can easily move in specific direction. This free moment of free electrons in particular direction under the influence of external field causes the flow of current in metal wires. The resistance of conductor increase in temperature. This is due to increase in the number of collision of electrons with themselves and with the atoms of the metals.

INSULATOR

 Insulator: All materials contain electrons. The electrons in insulator, like rubber, however, are not free to move. They are tightly bound inside atoms. Hence, current cannot flow through an insulator because there are not free electrons for the flow of current. Insulator have very large value of resistance. Insulator can easily charged by friction and the induced charged remains static on their surface. Other example of insulators are glass, wood, plastics, fur, silk, etc.

COMBINATION OF RESISTANCE

 Resistance can be connected in two ways.

(i) Series Combination

(ii) Parallel Combination 

(i) Series Combination

  In series combination, resistors are connected end to end and electric current has a single path through the circuit. This means that the current passing through each resistor is the same.

Equivalent Resistance of Series Circuit 

 The total voltages in a series circuit dividing among the individual resistors so the sum of the voltages across the resistance of each individual resistor is equal to the total voltages supplied by the source. Thus, we can write as

                                       V = V1 + V2 + V3

Where V is the voltages across the battery, and V1, V2, V3 are the voltages across resistors R1, R2 , R3 respectively. If I is the current passing through each resistor, Then from Ohm's Law

                                    

                                     

                                       V= IR1 + IR2 + IR3

                                       V= I(R1 + R2 + R3)

We can replace the combination of resistor with a single resistor is called Equivalent Resistance Re such that the same current passes through the circuit. From Ohm's law

                         

                                      V = IRe

Know equation becomes

                                      IRe =  I(R1 + R2 + R3)

                                      Re = R1 + R2 + R3 

Thus the equivalent resistance of the series combination is equal to the sum of the individual resistance of the combination.

If resistances R1, R2, R3,......., Rn are the connected in series, then the equivalent resistance of the combination will be given by

             

                                      Re = R1 +R2 + R3+......... + Rn

(ii) Parallel Combination 

   In parallel mix one end of every resistor is associated with positive terminal of the battery while the flip side of every resistor is associated with the negative terminal of the battery. Therefore, the voltages across the each resistor which is equal to the voltage of the battery i.e.,

    

                                  V =V1 =V2 =V3

Equivalent Resistance of Parallel Circuit

 In parallel circuit, the total current is equal the same of the currents in various resistances i.e.,

                 

                                I = I1 + I2 +I3

Since the voltages across each resistance is V, so by Ohm's law

                                 

                               I1= V/R1, I2 = V/R2 and I3 = V/R3

Thus the equation becomes

                              I = V/ R1 + V/R2 + VR3

                              I = V(1/R1 + 1/R2 + 1/R3)

We can replace the combination of resistors with a single resistor called equivalent resistance Re such that the same current passes through the circuit. From Ohm's law I = VRe. Thus the equation becomes 

                          V/Re = V [ 1/R1 + 1/R2 +1/R3

Thus the reciprocal of equivalent resistance of parallel combination is sum of the reciprocals of the individual resistances, which is less then the smallest resistance of the combination . If resistances R1, R2, R3,.....,Rn are connected in parallel then the equivalent resistance of the combination will be given by

                         1/Re = 1/R1 + 1/R2 + 1/R3+...............+1/Rn

Parallel circuits have two big advantages over series circuits. 

1. Each devices in the circuit receives the full battery voltages.

2. Each device in the circuit may be turned off independently without stopping the current flowing to the other devices in the circuit. This principle is used in household wiring.