 # Grouping of the cell's|Wheat stone bridge

## (6)Grouping of the cell's

• A limited ammount 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 emf's E1 and E2 and internal resistance r1 and r2 respectively connected in series combination through external resistance • Points A and B in the circuit acts as two terminals of the combination
• Applying kirchoff'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 (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 • Applying kirchoff's loop rule in loop containing E1 ,r1 and R,we find
E1-IR-I1r1=0 ------------------------(1)
Similarly applying kirchoff'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 We can rewrite this as E is the resulting EMF due to parallel combination of cells and r is resulting internal resistance.

(7) Wheat stone bridge
• Wheat stone bridge was designede by british physicist sir Charles F wheatstone in 1833
• It is a arrangement of four resistors used to determine resistance of one resistors in terms of other three resistors
• Consider the figure given below which is an arrangement of resistors and is knowns as wheat stone bridge • Wheatstone bridge consists of four resistance P,Q,R and S with a battery of EMF E.Two keys K1 and K2 are connected across terminals A and C and B and D respectively
• ON pressing key K1 fisrt and then pressing K2 next if galvanometer does not show any deflection then wheatstone bridge is said to be balanced
• Galavanometer is not showing any deflection this means that no current is flowing through the galvanameter and terminal B and D are at the same
potential .THus for a balanced bridge
VB=VD
• Now we have to find the condition for the balanced wheatstone bridge .For this applying kirchoff's loop rule to the loop ABDA ,we find the relation
-I2R+I1P=0
or I1P=I2R --(a)
Again applying kirchoff's rule to the loop BCDB
I1Q-I2S=0
or I1Q=I2S --(b)
From equation a and b we get
I1/I2=R/P=S/Q
or
P/Q=R/S                       (12)
• equation 12 gives the condition for the balanced wheatstone bridge
• Thus if the ratio of the resistance R is known then unknown resistance S can easily be calculated
• One important thing to note is that when bridge is balanced positions of cell and galvanometer can be exchanged without having any effect on the balance of the bridge
• Sensitivity of the bridge depends on the relative magnitudes of the resistance in the four arm of the bridge is maximum for same order of four resistance.