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:

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

The $I-V$ graph for a conductor at two different temperatures $100^{\circ} C$ and $400^{\circ} C$ is as shown in the figure. The temperature coefficient of resistance of the conductor is about (in per degree Celsius).

The resistance of a wire at $30^{\circ}C$ is $10\, \Omega$. To increase the resistance of the wire by $10\%$,the temperature should be .......... $^{\circ}C$. The temperature coefficient of resistance of the material of the wire is $0.002\, ^{\circ}C^{-1}$.

$A$ heating element using nichrome connected to a $230 \;V$ supply draws an initial current of $3.2 \;A$ which settles after a few seconds to a steady value of $2.8 \;A$. What is the steady temperature of the heating element if the room temperature is $27.0^{\circ} C$ (in $^{\circ} C$)? The temperature coefficient of resistance of nichrome averaged over the temperature range involved is $1.70 \times 10^{-4} \;^{\circ} C^{-1}$.

The resistance of the bulb filament is $100 \ \Omega$ at a temperature of $100^{\circ} C$. If its temperature coefficient of resistance is $0.005 \ ^{\circ} C^{-1}$,at what temperature will its resistance become $200 \ \Omega$ (in $^{\circ} C$)?