# Wheatstone's Bridge - 3

Key point:

• The accuracy of the post office box depends on the choice of the ratio arm

- for eg: if R_{2} : R_{1} = 1 : 1 then unknown resistance is obtained within ± 1

- of ratio R_{2} : R_{1} = 1 : 10 then unknown resistance is obtained within ± 0.1

- if ratio R_{2} : R_{1} = 1 : 100 then unknown resistance is obtained within ± 0.01

__Procedure__:

The unknown resistance X is connected to the post office box as shown in fig.14.5 Tke out 10 plugs from R_{1} and R_{2} without removing any plug from R. Press first the battery key K_{1} and then the galvanometer key K_{2} and note the direction of deflection in the galvanometer. Now, take out the infinity plug from R. Again, press the key K_{1} first and then the key K_{2} and note the direction of deflection of the galvanometer. If the galvanometer deflects in the opposite direction then the circuit, otherwise something in wrong with the circuit.

(i) Now press the key K_{1} and adjust the value of R for two consecutive values at which the galvanometer shows opposite deflections on pressing the key K_{2}. Note down the two values of R.

(ii) Now remove the 100 plug form R_{1} and maintaining R_{2} at 10 . Starting with 10 times the lower value of R obtained in the previous step, adjust its value to obtain two consecutive values for which the galvanometer shows opposite deflections on pressing the key K_{1} first and then the key K_{2}.

(iii) Now, make the value of R_{1} as 1000 and starting with 10 times the lower value of R obtained in the previous step, adjust the value of R so that the galvanometer shows deflections in the opposite directions by pressing the keys in the same order.

(iv) The value of the unknown resistance X lies in-between the two resistance obtained in the last step.

__Illustration__: The value of an unknown resistance is obtained by using a post office box. Two consecutive readings of R are observed at which the galvanometer deflects in thee opposite directions for three different vaalues of R_{1}. These two values are recorded under the column I and II in the following observation table:

]

S. No. | R_{1} () |
R_{2} () |
R lies in between | X = | ||
---|---|---|---|---|---|---|

I () | II () | I () | II () | |||

1. | 10 | 10 | 16 | 17 | ||

2. | 100 | 10 | 163 | 164 | ||

3. | 1000 | 10 | 1638 | 1639 |

Determine the value of the unknown resistance.

Solution:- The observation table may be completed as follows:

]

S. No. | R_{1} () |
R_{2} () |
R lies in between | X = | ||
---|---|---|---|---|---|---|

I () | II () | I () | II () | |||

1. | 10 | 10 | 16 | 17 | 16.0 | 17.0 |

2. | 100 | 10 | 163 | 164 | 16.3 | 16.4 |

3. | 1000 | 10 | 1638 | 1639 | 16.38 | 16.39 |