A copper wire is stretched to make it 0.5% lo | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The resistance $R$ of a wire is given by $R = \frac{\rho \ell}{A}$.Since the volume $V = A \ell$ remains constant,we can write $A = \frac{V}{\ell}

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(C) The resistance $R$ of a wire is given by $R = \frac{ho \ell}{A}$.Since the volume $V = A \ell$ remains constant,we can write $A = \frac{V}{\ell}$.Substituting this into the resistance formula: $R = \frac{ho \ell^2}{V}$.Since $ho$ and $V$ are constant,$R \propto \ell^2$.Taking the logarithmic derivative,we get $\frac{\Delta R}{R} = 2 \frac{\Delta \ell}{\ell}$.Given the percentage change in length $\frac{\Delta \ell}{\ell} 	imes 100 = 0.5\%$.Therefore,the percentage change in resistance is $\frac{\Delta R}{R} 	imes 100 = 2 	imes 0.5\% = 1\%$.

$A$ copper wire is stretched to make it $0.5\%$ longer. The percentage change in its electric resistance if its volume remains unchanged is ................ $\%$

Similar Questions

$A$ wire of length $5\,m$ and radius $1\,mm$ has a resistance of $1\,\Omega$. What length of the wire of the same material at the same temperature and of radius $2\,mm$ will also have a resistance of $1\,\Omega$?

The unit of specific resistance is

$A$ wire of resistance $R$ is stretched until its radius is halved. What will be the new resistance (in $, R$)?

Describe the effect of temperature on the electrical resistance of metals and semiconductors.

Two different conductors have the same resistance at $0\,^{\circ}C$. The resistance of the first conductor at $t_1\,^{\circ}C$ is equal to the resistance of the second conductor at $t_2\,^{\circ}C$. What is the ratio of their temperature coefficients of resistance $\alpha_1 / \alpha_2$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module