Question

A potentiometer wire 10 m long has a resistance of 40$\Omega$. It is connected in series with a resistance box and a 2V storage cell. If the potential gradient along the wire is 0.1 mV/cm , the resistance in the box is

• A. 760$\Omega$
• B. 260$\Omega$
• C. 1060$\Omega$
• D. 960$\Omega$

Answer 1

The correct option is A 760$\Omega$

PG$=0.1\frac{mV}{cm}$

$\Rightarrow \frac{△V}{l}=\frac{0.1\times {10}^{-3}}{1\times {10}^{-2}}$

$△V=l\times 0.01=0.1$

$\Rightarrow \frac{0.1}{2-0.1}=\frac{40}{R}$

$\Rightarrow R=760\Omega$