### Neet Solved Paper 2015 Question 28

##### Question: A potentiometer wire has length 4 m and resistance $ 8,\Omega $ . The resistance that must be connected in series with the wire and an accumulator of emf 2V, so as to get a potential gradient 1 mV per cm on the wire is

#### Options:

A) 32 $ \Omega $

B) 40 $ \Omega $

C) 44 $ \Omega $

D) 48 $ \Omega $

## Show Answer

#### Answer:

Correct Answer: A

#### Solution:

Given. 1 = 4 m, R = potentiometer wire resistance = $ 8\Omega $

Potential gradient = $ \frac{dV}{dr}=1mV/cm $ So, for $ 400cm,\Delta V=400\times 1\times {10^{-3}}=0.4V $

Let a resistor $ R _{s} $ connected in series, so as $ \Delta V=\frac{V}{R+R _{s}}\times R $

$ \Rightarrow 0.4=\frac{2}{8+R}\times 8\Rightarrow 8+R=\frac{16}{0.4}=40 $

$ \Rightarrow R=32,\Omega $