What equal length of an iron wire and a copper-nickel alloy wire, each of $2 \; {mm}$ diameter connected parallel to give an equivalent resistance of $3 \Omega ?$
(Given resistivities of iron and copper-nickel alloy wire are $12 \;\mu \Omega {cm}$ and $51\; \mu \Omega {cm}$ respectively) (in ${m}$)
JEE MAIN 2021, Diffcult
Download our app for free and get started
$\frac{{R}_{1} {R}_{2}}{{R}_{1}+{R}_{2}}=3$
$\frac{\left(12 \times 10^{-6} \times 10^{-2}\right) \ell \times 4}{\frac{\pi(2)^{2} \times 10^{-6}} \times \frac{\left(51 \times 10^{-6} \times 10^{-2}\right) \ell \times 4}{\pi(2)^{2} \times 10^{-6}}}{\frac{63 \times 10^{-6} \times 10^{-2} \times \ell \times 4}{\pi(2)^{2} \times 10^{-6}}}$
$\Rightarrow \ell=97 {m}$
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
- 1View SolutionTwo heating coils, one of fine wire and the other of thick wire of the same material and of the same length are connected in series and in parallel. Which of the following statement is correct
- 2The resistance of a wire is $R$. It is bent at the middle by $180^o$ and both the ends are twisted together to make a shorter wire. The resistance of the new wire isView Solution
- 3If current in an electric bulb changes by $1\%$, then the power will change by ............ $\%$View Solution
- 4A heating element has a resistance of $100\,\Omega $ at room temperature. When it is connected to a supply of $220\,V,$ a steady current of $2\,A$ passes in it and temperature is $500\,^oC$ more than room temperature. What is the temperature coefficient resistance of the heating element?View Solution
- 5A capacitor is connected to a cell of $emf$ $E$ having some internal resistance $r$. The potential difference across theView Solution
- 6Twelve resistors each of resistance $16 \,\Omega $ are connected in the circuit as shown. The net resistance between $AB$ (any two conjugate points of outer square) is ............... $\Omega$View Solution
- 7A battery has $e.m.f.$ $4\, V$ and internal resistance $r$. When this battery is connected to an external resistance of $2\, ohms$, a current of $1\, amp$. flows in the circuit. How much current will flow if the terminals of the battery are connected directly .......... $amp$View Solution
- 8Current of $4.8\,A$ is flowing through a conductor. The number of electrons per second will beView Solution
- 9View SolutionThe example for non-ohmic resistance is
- 10The equivalent resistance between $A$ and $B$ is $......$View Solution
