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

When the length and area of cross-section both are doubled,then its resistance

If copper and silicon are cooled from $300 \, K$ to $60 \, K$,their resistivity will:

$A$ wire of $1 \,\Omega$ has a length of $1\, m$. It is stretched until its length increases by $25\, \%$. The percentage change in resistance to the nearest integer is .....$\%$

$A$ metal wire of specific resistance $64 \times 10^{-6} \, \Omega \cdot \text{cm}$ and length $198 \, \text{cm}$ has a resistance of $7 \, \Omega$. The radius of the wire will be ............. $\text{cm}$.

The resistance of a wire is $5\, \Omega$ at $50\, ^\circ C$ and $6\, \Omega$ at $100\, ^\circ C$. The resistance of the wire at $0\, ^\circ C$ will be .............. $\Omega$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module