physicscatalyst.com logo




Grouping of the cell's





Grouping of the cell's

  • A limited amount of current can be drawn from a single cell or battery
  • There are situations where single cell fails to meet the current requirement in a circuits
  • To overcome the problem cells can be grouped in series and in parallel combinations or mixed grouping of cells is done in order to obtain a large value
    of electric current

(A) Series combination

  • Figure below shows the two cells of emfs E1 and E2 and internal resistance r1 and r2 respectively connected in series combination through external resistance

    Series combination of cells

  • Points A and B in the circuit acts as two terminals of the combination
  • Applying Kirchhoff's loop rule to above closed circuit
    -Ir2-Ir1-IR+E1+E2=0
    or
    I=E1+E2/R+(r1+r2)
    Where I is the current flowing through the external resistance R
  • Let total internal resistance of the combination by r=r1+r2 and also let E=E1+E2 is the total EMF of the two cells
  • Thus this combination of two cells acts as a cell of emf E=E1+E2 having total internal resistance r=r1+r2 as shown above in the figure

    Equivalent E of the series combination of cells

(B) Parallel combinations of cells

  • Figure below shows the two cells of emf E1 and E2 and internal resistance r1 and r2 respectively connected in parallel combination through external resistance
    Parallel combinations of cells

  • Applying Kirchhoff's loop rule in loop containing E1 ,r1 and R,we find
    E1-IR-I1r1=0 ------------------------(1)
    Similarly applying Kirchhoff's loop rule in loop containing E2 ,r2 and R,we find
    E2-IR-(I-I1)r2=0 ------------------------(2)
  • Now we have to solve equation 1 and 2 for the value of I,So multiplying 1 by r2 and 2 by r1 and then adding these equations results in following equation
    IR(r1+r2)+r2r1I-E1r2-E2r1=0
    which gives

    Grouping of the cell's|Wheat stone bridge
    We can rewrite this as
    Grouping of the cell's|Wheat stone bridge
    E is the resulting EMF due to parallel combination of cells and r is resulting internal resistance.



link to this page by copying the following text





Go back to Class 12 Main Page using below links
Class 12 Maths Class 12 Physics Class 12 Chemistry Class 12 Biology





Note to our visitors :-

Thanks for visiting our website.
DISCLOSURE: THIS PAGE MAY CONTAIN AFFILIATE LINKS, MEANING I GET A COMMISSION IF YOU DECIDE TO MAKE A PURCHASE THROUGH MY LINKS, AT NO COST TO YOU. PLEASE READ MY DISCLOSURE FOR MORE INFO.