A hollow cylindrical conductor has length of $3.14\,m$, while its inner and outer diameters are $4\,mm$ and $8\,mm$ respectively. The resistance of the conductor is $n \times 10^{-3}\,\Omega$.If the resistivity of the material is $2.4 \times 10^{-8}\,\Omega\,m$. The value of $n$ is $..........$
JEE MAIN 2023, Medium
Download our app for free and get started
$R =\rho \frac{\ell}{ A }$, the cross-sectional area is $\pi\left( b ^2- a ^2\right)$
$R =\rho \frac{\ell}{\pi\left( b ^2- a ^2\right)}=\frac{2.4 \times 10^{-8} \times 3.14}{3.14 \times\left(4^2-2^2\right) \times 10^{-6}}$
$=2 \times 10^{-3}\,\Omega$
$\rightarrow n =2$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1Three resistances of one ohm each are connected in parallel. Such connection is again connected with $\frac{2}{3}\,\Omega $ resistor in series. The resultant resistance will be ........... $\Omega$View Solution
- 2The current $I$ in the given circuit will be $......A$View Solution
- 3When the resistance $R$ (indicated in the figure below) is changed from $1 \,k \Omega$. to $10 \,k \Omega$, the current flowing through the resistance $R'$ does not change. What is the value of the resistor $R'?$View Solution
- 4The current $I$ flowing through the given circuit will be $.....A$.View Solution
- 5The current density is a solid cylindrical wire of radius $R ,$ as a function of radial distance $r$ is given by $J ( r )= J _{0}\left(1-\frac{ r }{ R }\right) .$ The total current in the radial region $r =0$ to $r =\frac{ R }{4}$ will beView Solution
- 6View SolutionAs the temperature of a conductor increases, its resistivity and conductivity change. The ratio of resistivity to conductivity
- 7Two cells of emf $E_1$ and $E_2\left(E_1 > E_2\right)$ are connected individually to a potentiometer and their corresponding balancing length are $625 \,cm$ and $500 \,cm$, then the ratio $\frac{E_1}{E_2}$ is ...........View Solution
- 8A student obtained following observations in an experiment of meter bridge to find the unknown resistance of the circuit The most accurate value of unknown resistance is ............ $\Omega$View Solution
S.No. $R$ $l$ $100-l$ $S = \left( {\frac{{100 - l}}{l}} \right)R$ $1$ $20\,\Omega $ $43$ $57$ $26.51\,\Omega $ $2$ $30\,\Omega $ $51$ $49$ $28.82\,\Omega $ $3$ $40\,\Omega $ $59$ $41$ $27.80\,\Omega $ $4$ $60\,\Omega $ $70$ $30$ $25.71\,\Omega $ - 9Find the power of the circuit ............ $W$View Solution
- 10In the following circuit, the battery has an emf of $2\mathrm{V}$ and an internal resistance of $\frac{2}{3}\ \Omega$. The power consumption in the entire circuit is$..... W.$View Solution
