Resistance Questions

A material $B$ has twice the specific resistance (resistivity) of $A$. A circular wire made of $B$ has twice the diameter of a wire made of $A$. For the two wires to have the same resistance, the ratio $L_A/L_B$ of their respective lengths must be:

The resistance of a bulb filament is $100\Omega$ at a temperature of $100^{\circ }\text{C}$. If its temperature coefficient of resistance be $0.005$ per ${}^{\circ }\text{C}$, its resistance will become $200\Omega$ at a temperature of:

The resistance of a wire is $5\Omega$ at $50^{\circ }\text{C}$ and $6\Omega$ at $100^{\circ }\text{C}$. The resistance of the wire at $0^{\circ }\text{C}$ will be:

The length of a given cylindrical wire is increased by $100\%$. Due to the consequent decrease in diameter, the percentage change in the resistance of the wire will be:

A $3\text{V}$ battery with negligible internal resistance is connected in a circuit as shown. (Circuit consists of three $3\Omega$ resistors, two in parallel, then in series with the third). The current $I$ in the circuit will be:

A $220\text{volt}$, $1000\text{watt}$ bulb is connected across a $110\text{volt}$ mains supply. The power consumed will be:

A strip of copper and another of germanium are cooled from room temperature to $80\text{K}$. The resistance of:

This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement 1: The temperature dependence of resistance is usually given as $R=R_0(1+\alpha \Delta t)$. The resistance of a wire changes from $100\Omega$ to $150\Omega$ when its temperature is increased from $27^{\circ }\text{C}$ to $227^{\circ }\text{C}$. This implies that $\alpha =2.5\times 10^{-3}{/}^{\circ }\text{C}$.
Statement 2: $R=R_i(1+\alpha \Delta T)$ is valid only when the change in the temperature $\Delta T$ is small and $\Delta R=(R-R_0)\ll R_0$.

Two conductors have the same resistance at $0^{\circ }\text{C}$ but their temperature coefficients of resistance are ${\alpha }_1$ and ${\alpha }_2$. The respective temperature coefficients of their series and parallel combinations are nearly:

If a wire is stretched to make it $0.1\%$ longer, its resistance will: