Two wires are made of the same material. The | vedclass

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

Question

(A) The resistance $R$ of a wire is given by the formula $R = \rho \frac{L}{A}$,where $\rho$ is the resistivity,$L$ is the length,and $A$ is the cross

Vedclass · Accepted Answer

Double the resistance of the second wire

Vedclass · Answer

(A) The resistance $R$ of a wire is given by the formula $R = ho \frac{L}{A}$,where $ho$ is the resistivity,$L$ is the length,and $A$ is the cross-sectional area. Since the area $A = \pi r^2 = \pi (d/2)^2 = \frac{\pi d^2}{4}$,we can write $R = ho \frac{4L}{\pi d^2}$. Let the first wire have length $L_1 = L$ and diameter $d_1 = d$. Its resistance is $R_1 = ho \frac{4L}{\pi d^2}$. For the second wire,$L_2 = 2L$ and $d_2 = 2d$. Its resistance is $R_2 = ho \frac{4(2L)}{\pi (2d)^2} = ho \frac{8L}{4\pi d^2} = ho \frac{2L}{\pi d^2}$. Comparing $R_1$ and $R_2$: $R_1 = 2 	imes (ho \frac{2L}{\pi d^2}) = 2 R_2$. Thus,the resistance of the first wire is double the resistance of the second wire.

Two wires are made of the same material. The length and diameter of the second wire are both double those of the first wire. What will be the resistance of the first wire compared to the second wire?

Similar Questions

$A$ wire of resistance $4 \,\Omega$ is stretched to twice its original length. The resistance of the stretched wire would be ........... $\Omega$.

Identify the correct statement among the following.

$A$ wire of resistance $5 \Omega$ is stretched so that its new length is $3$ times its original length. What is the resistance of the new wire?

$A$ metal wire of $1 \text{ cm}$ length and $1 \text{ mm}$ radius has a resistance of $3 \times 10^{-3} \Omega$. If a wire of the same metal of length $3 \text{ cm}$ and radius $0.5 \text{ mm}$ is drawn,what is the resistance of the new wire (in $\Omega$)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module