A metal wire of resistance $3\,\Omega $ is elongated to make a uniform wire of double its previous length. The new wire is now bent and the ends joined to make a circle. If two points on this circle make an angle $60^o$ at the centre, the equivalent resistance between these two points will be
JEE MAIN 2019, Medium
Download our app for free and get started
$R=\frac{\rho \ell}{A}=\frac{\rho \ell}{(V / \ell)}=\frac{\rho \ell^{2}}{V} \quad(V \rightarrow \text { Volume of wire })$
$\Rightarrow$ Final resistance $=3 \times(\mathrm{B})^{2}=12 \,\Omega$
$\begin{aligned} \mathrm{R}_{\mathrm{eq}} &=2\, \Omega \| 10\, \Omega \\ &=\frac{5}{3} \,\Omega \end{aligned}$
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
- 1In a potentiometer experiment the balancing with a cell is at length $240\,cm$ . On shunting the cell with a resistance of $2\,\Omega $ , the balancing length becomes $120\, cm$ . The internal resistance of the cell is ................... $\Omega$View Solution
- 2In a potentiometer experiment the balancing with a cell is at length $240\, cm$. On shunting the cell with a resistance of $2$ $\Omega$, the balancing length becomes $120\, cm$. The internal resistance of the cell is ................. $\Omega $View Solution
- 3A metal wire has a resistance of $35 \,\Omega$. If its length is increased to double by drawing it, then its new resistance will be (in $\Omega$)View Solution
- 4In the circuit shown in the adjoining figure, the current between $B$ and $D$ is zero, the unknown resistance is of ................ $\Omega$View Solution
- 5$A$ battery is of $\mathrm{emf}$ $E$ is being charged from a charger such that positive terminal of the battery is connected to terminal $A$ of charger and negative terminal of the battery is connected to terminal $B$ of charger. The internal resistance of the battery is $r$.View Solution
- 6Calculate the equivalent resistance between $A$ and $B$View Solution
- 7Three resistances, each of $1\, ohm$, are joined in parallel. Three such combinations are put in series, then the resultant resistance will be ............. $ohm$View Solution
- 8Find the equivalent resistance across the terminals of source of $e.m.f$. $24\, V$ for the circuit shown in figure .............. $\Omega$View Solution
- 9Each element in the finite chain of resistors shown in the figure is $\,1\,\Omega $ . A current of $1\, A$ flows through the final element. Then what is the potential difference $V$ across input terminals of the chain .................. $\mathrm{volt}$View Solution
- 10A storage battery has $e.m.f.$ $15\, volts$ and internal resistance $0.05\, ohm$. Its terminal voltage when it is delivering $10\, ampere$ is ............... $volts$View Solution