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Resistors in series|parallel combinations






(10)Combination of Resistors


  • We have earlier studied that sevral capacitors can be connected in series or parallel combination to form a network. In same way sevral resistor may be combined to form a network.
  • Just like capacitors resistors can be grouped in series and parallel.
  • Equivalent resistance of the combination of any number of resistors is a single resistance which draw same current as the combination of different resistances draw when the same potential difference is applied across it.

    (A) Resistors in Series
  • Resisors are said to be connected in series combinaton. If same current flows through each resistor when same potential difference is applied across the combination.
  • Consider the figure given below


    Resistors in Series

  • In figure given above three resistors if resistance R1, R2 and R3 are connected ibn series combination.
  • If battery is connected across the series combination so as to mintain potential difference V between points A and B, the current I would pass through each resistor.
  • If V1, V2 andV3 is the potential difference across each resistor R1, R2 and R3 respectively, then according to Ohm's Law,
    V1=IR1
    V2=IR2
    V3=IR3
    Since in series combination current remains same but potential is divieded so,
    V=V1+V2+V3
    or, V=I(R1+R2+R3)
    If Reqis the resistance equivalent to the series combination of R1, R2 and R3 then ,
    V=IReq
    where, Req=R1+R2+R3
  • Thus when the resistors are connected in series, equivalent resistance of the series combination is equal to the sum of individual resistances.
  • Value of esistance of the series combination is always greater then the value of largest individual resisnces.
  • For n numbers of resistors connected in series equivalent resistance would be
    Req=R1+R2+R3+...........................+Rn


    (B) Resistors in parallel
  • Resistors are said to be connected in parallel combination if potential difference across each resistors is same.
  • Thus , in parallel combination of resistors potential remains the same but current is divided.
  • Consider the figure given below

    Resistors in parallel

  • Battery B is connected across parallel combination of resistors so as to maintain potential difference V across each resistors.Then total current in the circuit would be
    I=I1+I2+I3                           (16)
  • Since potential difference across each resistors is V. Therefore, on applying Ohm's Law
    V=I1R1=I2R2=I3R3
    or,


    From equation (16)


  • If R is the equivalent resistance of parallel combination of three resistors heaving resistances R1, R2 and R3 then from Ohm's Law
    V=IReq
    or,

    Comparing equation (16) and (17) we get


  • For resistors connected in parallel combination reciprocal of equivalent resistance is equal to the sum of reciprocal of individual resistances.
  • Value of equivalent resistances for capacitors connected in parallel combination is always less then the value of the smallest resistance in circuit.
  • If there are n number of resistances connected in parallel combination, then quivalent resistance would be reciprocal of



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