Draw a circuit diagram for determining the unknown resistance R using meter bridge. Explain briefly its working, giving the necessary formula used.

Explanation

Practical form of wheatstone bridge is known as slidewise bridge metre bridge. Slide Wire Bridge: It is a device which is used find the unknown resistance of a conductor. It consists of a thin uniform wire AC made of manganin or eureka. It is one metre long. it is stretched and fixed between two thick copper strips at A and C and is placed along a metre scale over a wooden board. A jockey J is connected to the terminal D through a galvanometer G as shown in Fig. below. A resistance box is inserted in the gap between A and D with the help of which a known resistance R can be introduced between A and D. The resistance S to be determined is introduced between C and D. A cell is connected across A and C through a key K. To find the value of the unknown resistance, the key K is closed and a suitable resistance R is introduced in the resistance box. Now the jockey is moved along the wire till, for a certain position, the galvanometer shows zero deflection. Let B be this position. The points A, B, C and D correspond to the same points as on the Wheatstone bridge. The resistances of wire of lengths `AB (=l_(1)) and BC (=l_(2))` correspond to resistances P and Q respectively. Applying the principle of Wheatstone bridge, `(P)/(Q)= (R )/(S)` ...(I)

Since the wrie has a uniform area of cross-section, the resistances P and Q should be proportional to their respective lengths `l_(1) and l_(2)`.
So `(P)/(Q)= (l_(1))/(l_(2))`
But `l_(2)= 100-l_(1)`
`(P)/(Q)= (l_(1))/(100-l_(1))`
From eqn (i), we have `S= (Q)/(P) R`
`rArr S= ((100-l_(1))/(l_(1)))R`
So by knowing the balancing length `l_(1)` and R, we can find the unknown resistance S.