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Physics Question on Current electricity

If specific resistance of a potentiometer wire is 10−7 Ωm10^{-7}\, \Omega m and current flow through it is 0.1 amp., cross-sectional area of wire is 10−6 m210^{-6}\, m^2 then potential gradient will be

A

10−2  volt/m10^{-2}\, \, volt/ m

B

10−4  volt/m10^{-4}\, \, volt/ m

C

10−6  volt/m10^{-6}\, \, volt/ m

D

10−8  volt/m10^{-8}\, \, volt/ m

Answer

10−2  volt/m10^{-2}\, \, volt/ m

Explanation

Solution

Resistance of the potentiometer wire R=ρ1AR =\rho \frac{1}{ A }
Potential difference across the wire V=IlV = Il
So. potential gradient Vl=IRl=IρlAl\frac{ V }{ l }=\frac{ IR }{ l }=\frac{ I \rho l }{ Al }
Or Vl=IρA=0.1×10−710−6=0.01=10−2V/m\frac{ V }{ l }=\frac{ I \rho}{ A }=\frac{0.1 \times 10^{-7}}{10^{-6}}=0.01=10^{-2} V / m.