Wheatstone bridge

In this topic we will discuss about Wheatstone bridge ,its principle and balanced condition for Wheatstone bridge .And some important points for Wheatstone bridge.

Before to know about Wheatstone bridge , students must read these topics first-

i. Kirchhoff’s rule , to get the notes on this topic click here-

ii. Ohm’s law, to get the notes on this topic click here-

iii. Emf of the cells, To get the notes on this topic click here-

Wheatstone bridge –

It is an arrangement in which four resistances are arranged in the form of a bridge which is used for measuring one unknown resistance in terms of other three resistances .

Wheatstone bridge principle – It’s principle states that when four resistances P,Q,R and S are connected with a galvanometer and a cell in the form of bridge as shown in figure , the bridge is said to be balanced when there is no deflection shown by the galvanometer for this condition P/Q = R/S .

As shown in figure , resistance P is in arm AB , Q is in arm BC , R is in arm AD and S is in arm DC . A cell of emf ‘ε’ and galvanometer is connected as shown in figure with  keys K₁ and K₂ . On closing key K₁ and then key K₂ if galvanometer shows no deflection then it is said that bridge is balance , and we will get  P/Q = R/S  .

As shown in figure I is the current flowing through the cell , when it reaches to point A it divided in two parts I₁ towards AB and ( I-I₁ ) towards AD . Again when I₁ reaches to B then current I_g flows through galvanometer and ( I₁-I_g) towards C and current I-I₁+I_g towards DC .

Now applying Kirchhoff’s loop law in loop ABDA we get,

I₁P+I_gG-(I-I₁)R=0 …………………..(I)

Again from loop BCDB we get   (I₁-I_g)Q – ( I-I₁+I_g)S-I_gG=0………………(II)

If galvanometer shows no deflection i.e. I_g=0 then eq (ii) may be written as

I₁P  =  (I-I₁) R ………………….(III)

And eq. (ii) may be written as ,

I₁Q  =  (I-I₁) S ……………………..(IV)

Dividing (iii) by (iv) we get P/Q =R/S  This proves wheat-stone bridge .

Two view the video on Wheatstone bridge click here-

 

*****Important point for wheat-stone bridge ***

(1) Wheat-stone bridge is a null method , hence the measurement of unknown resistance is very accurate.

(2) Wheat-stone bridge remain unaffected by the internal resistance of the cell and galvanometer.

(3) it is not used to measure very high or very low resistances .

(4) It becomes very sensitive when  resistance of all four arms are nearly same .

 

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