# Wheat stone bridge

## Wheat stone bridge

- 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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