$A$ wire of $1 \,\Omega$ has a length of $1\, m$. It is stretched until its length increases by $25\, \%$. The percentage change in resistance to the nearest integer is .....$\%$

An electric wire of length $l$ and area of cross-section $a$ has a resistance $R \ \Omega$. Another wire of the same material having the same length and area of cross-section $4a$ has a resistance of:

$A$ piece of copper is to be shaped into a conducting wire of maximum resistance. If the initial length is $L$ and diameter is $d$,what should be the new length and diameter to achieve maximum resistance?

Two wires of the same material have lengths $L$ and $2L$ and cross-sectional areas $4A$ and $A$ respectively. The ratio of their specific resistance would be

Two metal wires of identical dimensions are connected in series. If $\sigma_1$ and $\sigma_2$ are the conductivities of the metal wires respectively,the effective conductivity of the combination is

$A$ cylindrical resistor is connected to a battery with emf $5 \ V$. The resistance per unit length varies as $\rho(x) = \rho_0 \left(\frac{x}{L}\right)^\alpha$,where $\rho_0$ and $\alpha$ are constants and $x$ is the distance from one end of the resistor. The product $\rho_0 L$ is $10 \ \Omega$,where $L$ is the length of the resistor. If the thermal power generated by the resistor is $20 \ W$,then the value of $\alpha$ is: