Two conductors are made of the same material | vedclass

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

Question

(C) Resistance of a conductor is given by $R = \frac{\rho l}{A}$,where $\rho$ is resistivity,$l$ is length,and $A$ is the cross-sectional area.For con

Vedclass · Accepted Answer

$3:1$

Vedclass · Answer

(C) Resistance of a conductor is given by $R = \frac{ho l}{A}$,where $ho$ is resistivity,$l$ is length,and $A$ is the cross-sectional area.For conductor $A$ (solid wire of diameter $d_A = 1 \ mm$):Radius $r_A = 0.5 \ mm = 0.5 	imes 10^{-3} \ m$.Area $A_A = \pi r_A^2 = \pi (0.5 	imes 10^{-3})^2 = 0.25 \pi 	imes 10^{-6} \ m^2$.$R_A = \frac{ho l}{0.25 \pi 	imes 10^{-6}} = \frac{4 ho l}{\pi 	imes 10^{-6}}$....$(1)$For conductor $B$ (hollow tube of outer diameter $D_B = 2 \ mm$ and inner diameter $d_B = 1 \ mm$):Outer radius $R_{out} = 1 \ mm = 10^{-3} \ m$,inner radius $r_{in} = 0.5 \ mm = 0.5 	imes 10^{-3} \ m$.Area $A_B = \pi (R_{out}^2 - r_{in}^2) = \pi ((10^{-3})^2 - (0.5 	imes 10^{-3})^2) = \pi (1 - 0.25) 	imes 10^{-6} = 0.75 \pi 	imes 10^{-6} \ m^2$.$R_B = \frac{ho l}{0.75 \pi 	imes 10^{-6}} = \frac{4 ho l}{3 \pi 	imes 10^{-6}}$....$(2)$Taking the ratio $\frac{R_A}{R_B}$:$\frac{R_A}{R_B} = \frac{4 ho l}{\pi 	imes 10^{-6}} 	imes \frac{3 \pi 	imes 10^{-6}}{4 ho l} = \frac{3}{1}$.Thus,$R_A : R_B = 3 : 1$.

Two conductors are made of the same material and have the same length. Conductor $A$ is a solid wire of diameter $1 \ mm$. Conductor $B$ is a hollow tube of outer diameter $2 \ mm$ and inner diameter $1 \ mm$. Find the ratio of resistance $R_A$ to $R_B$.

Similar Questions

The resistance of a resistor wire is $5 \, \Omega$ at $50^{\circ}C$ and $6 \, \Omega$ at $100^{\circ}C$. What is its resistance at $0^{\circ}C$ in $\Omega$?

Explain the qualitative dependence of resistivity on temperature.

$A$ $1\,m$ long wire is broken into two unequal parts $X$ and $Y$. The $X$ part of the wire is stretched into another wire $W$. The length of $W$ is twice the length of $X$ and the resistance of $W$ is twice that of $Y$. Find the ratio of the length of $X$ to the length of $Y$.

$A$ thick wire is stretched so that its length becomes two times. Assuming that there is no change in its density,what is the ratio of the change in resistance of the wire to the initial resistance of the wire?

If a wire of resistance $R$ is melted and recasted to half of its length,then the new resistance of the wire will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module