The cross-sections of wires made of the same | vedclass

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

Question

(A) The resistance of a wire is given by $R = \rho \frac{l}{A}$,where $\rho$ is the resistivity,$l$ is the length,and $A$ is the cross-sectional area.

Vedclass · Accepted Answer

$R_A = R_B = R_C$

Vedclass · Answer

(A) The resistance of a wire is given by $R = \rho \frac{l}{A}$,where $\rho$ is the resistivity,$l$ is the length,and $A$ is the cross-sectional area.Since all wires are made of the same material ($\rho$ is constant) and have the same length ($l$ is constant),the resistance depends only on the cross-sectional area $A$.For wire $A$: The cross-section is a square frame with outer side $\sqrt{3}a$ and inner side $\sqrt{2}a$. Area $A_A = (\sqrt{3}a)^2 - (\sqrt{2}a)^2 = 3a^2 - 2a^2 = a^2$.For wire $B$: The cross-section is a square frame with outer side $\sqrt{2}a$ and inner side $a$. Area $A_B = (\sqrt{2}a)^2 - (a)^2 = 2a^2 - a^2 = a^2$.For wire $C$: The cross-section is a solid square with side $a$. Area $A_C = a^2$.Since $A_A = A_B = A_C = a^2$,it follows that $R_A = R_B = R_C$.

The cross-sections of wires made of the same material and having the same length are shown in the figure. What can be said about their resistances?

Similar Questions

The masses of three wires of copper are in the ratio of $1 : 3 : 5$ and their lengths are in the ratio $5 : 3 : 1.$ The ratio of their electrical resistances is

The resistance of a wire is $20 \Omega$. It is stretched,so that the length becomes three times,then the new resistance of the wire will be (in $\Omega$)

$A$ silver wire has a resistance of $2.1\; \Omega$ at $27.5^{\circ} C$ and a resistance of $2.7\; \Omega$ at $100^{\circ} C$. Determine the temperature coefficient of resistivity of silver.

By increasing the temperature,the specific resistance (resistivity) of a conductor and a semiconductor,respectively,is:

The length of a given cylindrical wire is increased by $100\,\%$. Due to the consequent decrease in diameter,the percentage change in the resistance of the wire will be ................ $\%$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module