Explain how value of unknown resistor can be obtained by using meter bridge.

Explanation

In one gap of meter bridge unknown resistor R and in second gas resistance S from resistance box is connected.
Jockey key is slided (moved) on wire AC.
`rArr` Assume that when jockey key is on position D, galvanometer shows zero deflection.
`rArr` Let length from A to D is l.
`rArr` Resistance of AD wire = `R_(cm)` l where `R_(cm)` is resistance of wire per unit length (1 cm).
`therefore ` Resistance of DC wire = `R_(cm) ` (100 - l)
`rArr` Wire AB, BC, DA and CD form Wheatstone bridge, where, AB = R, BC = S, DA = `R_(cm)` l
CD = `R_(cm) (100 - l) `
From principle of Wheatstone bridge for balancing of Wheatstone bridge,
` (AB)/(BC) = (DA)/(CD)`
`therefore (R)/(S) = (R_(cm)l)/(R_(cm) (100 - l))`
`therefore (R)/(S) = (l)/(100 -l)`
`rArr` Unknown resistance can be obtained by using equation R = `S (l)/(100 - l)`.
`rArr` For different value of S, value of unknown resistance R can be obtained by taking average value error can be eliminated.
`rArr` To eliminate end correction. position of resistance R and resistance S from box can be interchanged and null point can be obtained and error can be reduced.
`rArr` For balancing bridge, null point should be at 50 cm (between 40 cm and 60 cm) and percentage error can be minimized.
`rArr` From value of resistance obtained by meter bridge temperature of unknown resistance can be obtained.
`rArr` By using meter bridge value of small resistance can be known.