The Wheatstone bridge, i.e., the circuit shown in the figure is used to determin

Question

The Wheatstone bridge, i.e., the circuit shown in the figure is used to determine the value of an unknown resistor R x by comparison with the resistors R1 , R 2 . and R 3 whose resistances can be varied. For each setting the resistance o f each resistor is precisely known. With switches S l and S 2 closed, these resistors arc varied until the current in the galvanometer G is zero. When the galvanometer shows the zero current, we say that the bridge is balanced. This method permits very high precision in comparing resistors. Under the condition o f the balanced bridge, derive expression for the unknown resistance R x in terms of the known resistances R 1, R 2, and R 3 . Verify that when R , = 1 5 ohm, R 2 = 3 0 ohm, and R3 = 850 ohm, the unknown resistance must be 1.7k ohm.

Explanation / Answer

when it is balanced :

no current goes through G

let I1 be current in ab and I2 be current in R2

by mesh law in loop abcI1R1=I2R2

and in bcd I1R3 =I2 Rx

dividing both these results we get

R1/R2 = R3/Rx

hence proved

implies

Rx= (850 )*(30/15)= 1700ohms =1.7kohm

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