In a standard meter bridge experiment, to measure the specific resistance of a wire the following data are found:- 

Length $\left(\mathrm{L}\right)=(1\pm .01)$m measured by a meter scale 
Radius of wire $=1\mathrm{mm}\pm .01\mathrm{mm}$ (measured by screw gauge).
Resistance of wire $\left(R\right)=(5\pm .01)\mathrm{\Omega }$
The maximum possible error in the measurement of specific resistance is
(You may use the formula:- $\left.:-\mathrm{\rho }=\frac{{\mathrm{\pi r}}^2}{\mathrm{L}}\mathrm{R}\right)$

In a meter bridge experiment, the specific resistance (ρ) of a wire is calculated using the formula:

ρ = πr²LR

Given data from the meter bridge experiment:

• Length of the wire (L) = (1 ± 0.01) m
• Radius of the wire (r) = (1 ± 0.01) mm = (0.001 ± 0.00001) m
• Resistance of the wire (R) = (5 ± 0.01) Ω

First, calculate the specific resistance:

ρ = π × r² × L × R

Substitute the values:

ρ = 3.14 × (0.001)² × 1 × 5

ρ = 3.14 × 10^-6 × 5

ρ = 15.7 μΩ·m

Next, calculate the maximum possible error (δρ) using the formula:

δρ = ρ × [(2 × δr/r) + (δL/L) + (δR/R)]

Substitute the values:

δρ = 15.7 × 10^-6 × [(2 × 0.00001/0.001) + (0.01/1) + (0.01/5)]

δρ = 15.7 × 10^-6 × [0.02 + 0.01 + 0.002]

δρ = 15.7 × 10^-6 × 0.032

δρ = 0.5024 μΩ·m

Final Results

• Specific resistance (ρ): 15.7 μΩ·m
• Maximum possible error (δρ): 0.5024 μΩ·m

Thus, the calculated specific resistance and its maximum possible error align with the results obtained during the meter bridge experiment.