$A$ wire of resistance $R$ is elongated $n$-fold to make a new uniform wire. What is the resistance of the new wire?

Explain how the resistance of a conductor depends on its dimensions.

$A$ heating element has a resistance of $100\,\Omega$ at room temperature. When it is connected to a supply of $220\,V$,a steady current of $2\,A$ passes through it and the temperature is $500\,^{\circ}C$ higher than room temperature. What is the temperature coefficient of resistance of the heating element?

Choose the correct alternative:
$(a)$ Alloys of metals usually have (greater/less) resistivity than that of their constituent metals.
$(b)$ Alloys usually have much (lower/higher) temperature coefficients of resistance than pure metals.
$(c)$ The resistivity of the alloy manganin is nearly independent of/ increases rapidly with increase of temperature.
$(d)$ The resistivity of a typical insulator (e.g.,amber) is greater than that of a metal by a factor of the order of $(10^{22}/10^{23}).$

The resistance of a wire is $20 \, \Omega$. It is stretched such that its length becomes three times its original length. The new resistance of the wire will be ............. $ \Omega$.

The specific resistance (resistivity) of manganin is $50 \times 10^{-8} \, \Omega \cdot m$. The resistance of a cube of length $50 \, cm$ will be: