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  • In a meter bridge experiment, a uniform wire of unknown length L and cross sectional area A = 2×10−6 m2 is used. The bridge is balanced with a standard resistor of

In a meter bridge experiment, a uniform wire of unknown length L and cross sectional area A = 2×10−6 m2 is used. The bridge is balanced with a standard resistor of 6 ohms in one gap and the unknown wire in the other gap. The length of the unknown wire on the side of the standard resistor is 0.8 meters. If the bridge is balanced at a jockey position 0.4 meters from the left end of the unknown wire, determine the resistivity (ρ) of the wire material. Express your answer in terms of fundamental constants and known quantities.

Option: 1

2 ×10−5ohm


Option: 2

9×10−5 ohm


Option: 3

35 ×10−5ohm


Option: 4

15 ×10−5ohm


Answers (1)

best_answer

1. The formula for resistance (R) of a wire is given by:R=\rho\left(\frac{l}{A}\right) \text {, where } \rho is the resistivity of the material, l is the length of the wire, and A is the cross-sectional area of the wire.

2. Given the length of the unknown wire on the side of the standard resistor (l1) is 0.8 meters, and the jockey position (x) is 0.4 meters from the left end, we can find the length of the wire on the other side as l2 = L − l1 = L − 0.8 meters.

3. The bridge is balanced when the ratio of the resistances on the two sides is equal:\frac{R_1}{R_2}=\frac{l_1}{l_2}

\text { 4. Substituting the values: } \frac{6}{R_2}=\frac{0.8}{L-0.8} \text {. }

\text { 5. Solving for } R_2 \text {, we find: } R_2=\frac{6(L-0.8)}{0.8} \text { ohms. }6. Substituting the values into the resistance formula for l_2: \rho\left(\frac{l_2}{A}\right)=\frac{6(L-0.8)}{0.8}

\text { 7. Solving for } \rho: \rho=\frac{6(L-0.8) A}{0.8 l_2} \text {. }

8. Substituting the values of A and l_2: \rho=\frac{6(L-0.8) \times 2 \times 10^{-6}}{0.8(L-0.8)} \text {. }

\text { 9. Simplifying: } \rho=\frac{12 \times 10^{-6}}{0.8} \text { ohm meter. }

Therefore, the resistivity of the unknown wire material is 15 × 10−6 ohm meter. Therefore, the correct option is 4.

Posted by

sudhir.kumar

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