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Measurement of an unknown resistance using a Post Office Box

A Post Office Box can also be used to measure an unknown resistance. It is a Wheatstone Bridge with three arms P, Q and R; while the fourth arm(s) is the unknown resistance. P and Q are known as the ratio arms while R is known as the rheostat arm.

 At balance, the unknown resistance

         S = (P/Q) R                                                           …… (1)

 The ratio arms are first adjusted so that they carry 100 W each. The resistance in the rheostat arm is now adjusted so that the galvanometer deflection is in one direction. If R = R0 (ohm) and
R = R0 + 1 (ohm) are the resistance in rheostat arm, for which the deflection in galvanometer is in opposite direction, then it implies that the unknown resistance ‘s’ lies between R0 & (R0 + 1) ohm.

 1764_resistance-using-post-office-box.jpg

                                     Alt txt: resistance-using-post-office-box

Now, the resistance in P and Q are made 100 W and 1000 W, respectively, and the process is repeated. Equation (1) is used to compute S. The ratio P/Q is progressively made 1:10, and then 1:100. Thus, the resistance S can be accurately measured.

 Errors

 The major sources of error are the connecting wires, unclear resistance plugs, change in resistance due to Joule heating, and the insensitivity of the Wheatstone bridge

These errors may be removed by using thick connecting wires, clean plugs, keeping the circuit on for very brief periods (to avoid Joule heating) and calculating the sensitivity.

In order that the sensitivity is maximum, the resistance in the arm P is kept close to the value of the resistance S.

 Illustration:

 Resistance of a conductor is 1.72 W at a temperature of 20oC. Find the resistance at 0oC and 100oC. Given the coefficient of resistivity is
a = 0.00393/oC.

 Solution:

        R = R0 (1 + aDT)

        R = 1.72 W (1 + 0.00393) × (0oC – 20oC) = 1.58 W

        At T = 100oC

        R = 1.72 W [1 + 0.00393) × (100oC – 20oC)] = 2.26 W

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