$A$ wire of radius $r$ has resistance $R$. If it is stretched to a radius of $\frac{3r}{4}$,its resistance becomes

$A$ tapered bar of length $L$ and end diameters $D_1$ and $D_2$ is made of a material of electrical resistivity $\rho$. The electrical resistance of the bar is

The resistivity of iron is $1 \times 10^{-7} \, \Omega \cdot m$. The resistance of an iron wire of a particular length and thickness is $1 \, \Omega$. If the length and the diameter of the wire are both doubled, then the resistivity in $\Omega \cdot m$ will be:

We have two wires $A$ and $B$ of the same mass and same material. The diameter of wire $A$ is half that of wire $B$. If the resistance of wire $A$ is $24 \, \Omega$,then the resistance of wire $B$ will be ................ $\Omega$.

The power of a heater is $500 \ W$ at a temperature of $800 \ ^oC$. What will be its power at $200 \ ^oC$ in $W$? Given $\alpha = 4 \times 10^{-4} \ ^oC^{-1}$.

Two square-shaped metal plates $A$ and $B$ of the same thickness $(t)$ and of the same material are connected as shown in the figure. The side of $B$ is twice that of $A$. If the resistances of $A$ and $B$ are $R_A$ and $R_B$ respectively, then $\frac{R_A}{R_B}$ is: