An unknown length of platinum wire 0.760mm in diameter is placed as the unknown

Question

An unknown length of platinum wire 0.760mm in diameter is placed as the unknown resistance in a Wheatstone bridge (see the figure (Figure 1) ). Arms 1 and 2 have resistance of 38.0? and 55.0? , respectively. Balance is achieved when R3 is 3.63? . Resistivity of platinum is 10.6*10^-8

An unknown length of platinum wire 0.760mm in diameter is placed as the unknown resistance in a Wheatstone bridge (see the figure (Figure 1) ). Arms 1 and 2 have resistance of 38.0? and 55.0? , respectively. Balance is achieved when R3 is 3.63? . Resistivity of platinum is 10.6*10^-8 How long is the platinum wire?

Explanation / Answer

for a balance wheat stone bridge

R3/R1 = Rx / R2

3.63 / 38 = Rx / 55

Rx = 5.2539 ohm

R = pho x L/A

A = pi x d^2 = 3.14 x .76/1000^2 = 1.81 x 10^-6 m^2

rho = 10.6 x 10^-8

5.2539 = 10.6 x 10^- 8 x L / 1.81 x 10^-6

L = 89.89 m

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