Masses of 3 wires of same metal are in the ra | vedclass

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

Question

(D) The resistance $R$ of a wire is given by $R = \rho \frac{l}{A}$.Since $Volume = V = A \cdot l$,we have $A = \frac{V}{l}$.Also,$Mass = m = d \cdot

Vedclass · Accepted Answer

$27:6:1$

Vedclass · Answer

(D) The resistance $R$ of a wire is given by $R = \rho \frac{l}{A}$.Since $Volume = V = A \cdot l$,we have $A = \frac{V}{l}$.Also,$Mass = m = d \cdot V$,where $d$ is the density. Thus,$V = \frac{m}{d}$.Substituting $A$ in the resistance formula: $R = \rho \frac{l}{(m/dl)} = \rho \cdot d \cdot \frac{l^2}{m}$.Since the material is the same,$\rho$ and $d$ are constant,so $R \propto \frac{l^2}{m}$.Given ratios: $m_1:m_2:m_3 = 1:2:3$ and $l_1:l_2:l_3 = 3:2:1$.Therefore,the ratio of resistances is $R_1:R_2:R_3 = \frac{l_1^2}{m_1} : \frac{l_2^2}{m_2} : \frac{l_3^2}{m_3}$.$R_1:R_2:R_3 = \frac{3^2}{1} : \frac{2^2}{2} : \frac{1^2}{3} = 9 : 2 : \frac{1}{3}$.Multiplying by $3$ to clear the fraction: $27 : 6 : 1$.

Masses of $3$ wires of same metal are in the ratio $1 : 2 : 3$ and their lengths are in the ratio $3 : 2 : 1$. The electrical resistances are in ratio

Similar Questions

In the given circuit,the lengths of $AB$ and $BC$ are equal. The radius of $AB$ is three times that of $BC$. What is the ratio of the potential difference across $AB$ to that across $BC$?

The resistance of a wire is $20 \, \Omega$. It is stretched such that its length becomes three times its original length. The new resistance of the wire will be ............. $ \Omega$.

The resistance of a platinum wire at $0^{\circ}C$ is $2\,\Omega$ and $6.8\,\Omega$ at $80^{\circ}C$. The temperature coefficient of resistance of the wire is:

As the temperature increases,the electrical resistance:

$A$ rod of a certain metal is $1.0 \, m$ long and $0.6 \, cm$ in diameter. Its resistance is $3.0 \times 10^{-3} \, \Omega$. Another disc made of the same metal is $2.0 \, cm$ in diameter and $1.0 \, mm$ thick. What is the resistance between the round faces of the disc?

Vedclass Test Series

Exam Paper Generator

Online Exam Module