$n$ conducting wires of same dimensions but having resistivities $1, 2, 3, . . . , n$ are connected in series. The equivalent resistivity of the combination is

$A$ platinum resistance thermometer has a resistance of $50\,\Omega$ at $20\,^{\circ}C$. When dipped in a liquid,the resistance becomes $76.8\,\Omega$. The temperature coefficient of resistance for platinum is $\alpha = 3.92 \times 10^{-3}\,^{\circ}C^{-1}$. The temperature of the liquid is .............. $^{\circ}C$.

Wires $A$ and $B$ have resistivities $\rho_A$ and $\rho_B$,where $\rho_B = 2 \rho_A$,and have lengths $l_A$ and $l_B$. If the diameter of wire $B$ is twice that of $A$ and the two wires have the same resistance,then the ratio $\frac{l_B}{l_A}$ is:

$A$ 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 length of the resistance wire is increased by $10\%$. What is the corresponding change in the resistance of the wire? ................ $\%$

$A$ copper wire is stretched to make it $0.5\%$ longer. The percentage change in its electric resistance if its volume remains unchanged is ................ $\%$