Current Electricity 4 Question 2

2. In the circuit shown, a four-wire potentiometer is made of a $400 cm$ long wire, which extends between $A$ and $B$. The resistance per unit length of the potentiometer wire is $r=0.01$ $\Omega / cm$. If an ideal voltmeter is connected as shown with jockey $J$ at $50 cm$ from end $A$, the expected reading of the voltmeter will be

(a) $0.20 V$

(b) $0.75 V$

(c) $0.25 V$

(d) $0.50 V$

Show Answer

Solution:

  1. In given potentiometer, resistance per unit length is $x=0.01 \Omega cm^{-1}$.

Length of potentiometer wire is $L=400 cm$

Net resistance of the wire $A B$ is

$R _{A B}=$ resistance per unit length $\times$ length of $A B$

$$ =0.01 \times 400 $$

$$ \Rightarrow \quad R _{A B}=4 \Omega $$

Net internal resistance of the cells connected in series,

$$ r=0.5+0.5=1 \Omega $$

$\therefore$ Current in given potentiometer circuit is

$$ \begin{aligned} I & =\frac{\text { Net emf }}{\text { Total resistance }}=\frac{\text { Net emf }}{r+R+R _{A B}} \\ & =\frac{3}{1+1+4}=0.5 A \end{aligned} $$

Reading of voltmeter when the jockey is at $50 cm\left(l^{\prime}\right)$ from one end $A$,

$$ \begin{aligned} V & =I R=I\left(x l^{\prime}\right) \\ & =0.5 \times 0.01 \times 50=0.25 V \end{aligned} $$



NCERT Chapter Video Solution

Dual Pane