The following four wires are made of the same | 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

Length = $50 \ cm$,diameter = $0.5 \ mm$

Vedclass · Answer

(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-sectional area.Since $A = \pi r^2 = \pi (d/2)^2 = \frac{\pi d^2}{4}$,we have $R \propto \frac{l}{d^2}$.For option $A$: $R_A \propto \frac{50}{(0.5)^2} = \frac{50}{0.25} = 200$.For option $B$: $R_B \propto \frac{100}{(1)^2} = 100$.For option $C$: $R_C \propto \frac{200}{(2)^2} = \frac{200}{4} = 50$.For option $D$: $R_D \propto \frac{300}{(3)^2} = \frac{300}{9} \approx 33.3$.Comparing these values,the ratio $\frac{l}{d^2}$ is maximum for option $A$. Therefore,the wire in option $A$ has the highest electrical resistance.

The following four wires are made of the same material and are at the same temperature. Which one of them has the highest electrical resistance?

Similar Questions

Resistivity of which of the following substances decreases on increasing the temperature?

The range of electrical conductivity $(\sigma)$ and resistivity $(\rho)$ for metals,among the following,is

Wires $P$ and $Q$ have the same resistance at room temperature. When heated,the resistance of $P$ increases and that of $Q$ decreases. We conclude that:

Resistance of a tungsten wire at $150\,^{\circ}C$ is $133\,\Omega$. Its resistance temperature coefficient is $0.0045\,^{\circ}C^{-1}$. The resistance of this wire at $500\,^{\circ}C$ will be .............. $\Omega$.

The resistances of a carbon filament lamp and a tungsten filament lamp are measured individually when the lamps are lit and compared with their respective resistances when cold. Which one of the following statements will be true?

Vedclass Test Series

Exam Paper Generator

Online Exam Module