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Resistors in Series - (Concept)

Resistance of a system of resistors

  • We know that current through a conductor depends upon its resistance and potential difference across its ends.

  • In various electrical instruments, resistors are often used in various combinations and Ohm’s Law can be applied to combinations of resistors to find the equivalent resistance of the combination.

  • The resistances can be combined in two ways

    1. In series

    2. In parallel

  • To increase the resistance individual resistances are connected in series combination and to decrease the resistance individual resistances are connected in parallel combination.

     

Resistors in Series

  • When two or more resistances are connected end to end then they are said to be connected in series combination.

  • The figure below shows a circuit diagram where two resistors are connected in a series combination.


 

                    

                                                                            (Figure - 7.1)

 

  • Now the value of current in the ammeter is the same irrespective of its position in the circuit. So we conclude that " For a series combination of resistors the current is same in every part of the circuit or same current flows through each resistor "

Again if we connect three voltmeters one across each resistor as shown below in the figure given below. The potential difference measured by voltmeter across each one of resistors R1 , R2 and R3 is V1 , V2 and V3 respectively and if we add all these potential differences then we get

                                                                             $V=V_1+V_2+V_3$                              (7)

                              

                                                                          (Figure - 7.2)

  • This total potential difference V in the above equation is measured to be equal to potential difference measured across points X and Y that is across all the three resistors in the first figure (7.1). So, we conclude that <"the total potential difference across a combination of resistors in series is equal to the sum of potential differences across the individual resistors."

  • Again consider figure 7.2 where I is the current flowing through the circuit which is also the current through each resistor. If we replace three resistors joined in series by an equivalent single resistor of resistance R such that the potential difference V across it, and the current I through the circuit remains the same.

  • Now applying Ohm’s law to entire circuit we get

          V=I R

    On applying Ohm's law to the three resistors separately we have,

    $$
    \begin{aligned}
    & V_1=I R_1 \\
    & V_2=I R_2 \\
    & V_3=I R_3
    \end{aligned}
    $$


    From equation 7

    $$
    \begin{aligned}
    & I R=I R_1+I R_2+I R_3 \\
    & R=R_1+R_2+R_3
    \end{aligned}
    $$

    So here from the last equation, we conclude that when several resistances are connected in series combination, the equivalent resistance equals the sum of their individual resistances and is thus greater than any individual resistance.


     

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