A uniform metallic wire carries a current $2 \mathrm{A}$, when $3.4 \mathrm{V}$ battery is connected across it. The mass of uniform metallic wire is $8.92\times {10}^{-3} \mathrm{kg}$, density is $8.92\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$ and resistivity is $1.7\times {10}^{-8} \mathrm{\Omega }-\mathrm{m}$  The length of wire is : 

In the given circuit, the equivalent resistance between the terminal A and B is ____ $\mathrm{\Omega }$

Two cells are connected between points $A$ and $B$ as shown. Cell 1 has emf of $12 \mathrm{V}$ and internal resistance of $3 \mathrm{\Omega }$. Cell 2 has emf of $6 \mathrm{V}$ and internal resistance of $6 \mathrm{\Omega }$. An external resistor $R$ of $4 \mathrm{\Omega }$ is connected across $A$ and $B$. The current flowing through $R$ will be ______ $\mathrm{A}$.

With the help of potentiometer, we can determine the value of emf of a given cell. The sensitivity of the potentiometer is

(A) directly proportional to the length of the potentiometer wire

(B) directly proportional to the potential gradient of the wire

(C) inversely proportional to the potential gradient of the wire

(D) inversely proportional to the length of the potentiometer wire

Choose the correct option for the above statements: