Wheat stone bridge was designed 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 K_{1} and K_{2} are connected across terminals A and C and B and D respectively
ON pressing key K_{1} first and then pressing K_{2} next if galvanometer does not show any deflection then Wheatstone bridge is said to be balanced
Galvanometer is not showing any deflection this means that no current is flowing through the galvanometer and terminal B and D are at the same
potential .THus for a balanced bridge
V_{B}=V_{D}
Now we have to find the condition for the balanced Wheatstone bridge .For this applying Kirchhoff's loop rule to the loop ABDA ,we find the relation
-I_{2}R+I_{1}P=0
or I_{1}P=I_{2}R --(a)
Again applying Kirchhoff's rule to the loop BCDB
I_{1}Q-I_{2}S=0
or I_{1}Q=I_{2}S --(b)
From equation a and b we get
I_{1}/I_{2}=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.
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