Three students Shweta, Ayesha and Samridhi were performing an experiment to understand the factors on which the resistance of a conductor depends. Each one of them completed electric circuit with the help of a cell, an ammeter, a plug key and wire. Shweta put nichrome wire of length 'l' in the circuit. Ayesha put nichrome wire of same thickness but twice the length i.e. '2l'. Samridhi took copper wire of length 'l' and same thickness.

(a) If the ammeter reading is X ampere with nichrome wire of length 'l', then what will be the ammeter reading if the length of nichrome wire is doubled with same area of cross-section?

(b) What happens to the ammeter reading if the area of cross-section of nichrome wire is doubled, keeping the length of wire 'l' the same?

(c) Define 'resistivity'. Write its SI unit. Compare the resistivity of an alloy with its constituents metals.

OR

(c) Give reason:

(i) Tungsten is used almost exclusively for making the filament of electric lamps.

(ii) Conductors of bread-toasters are made of an alloy rather than a pure metal.

The resistance of a wire is $R = \dfrac{\rho L}{A}$ and the current is $I = \dfrac{V}{R}$.

(a) Doubling the length (same area) doubles the resistance ($R \propto L$). Since $I \propto \dfrac{1}{R}$, the current becomes half. Ammeter reading $= \dfrac{X}{2}$ ampere.

(b) Doubling the area of cross-section (same length) halves the resistance ($R \propto \dfrac{1}{A}$), so the current doubles. Ammeter reading becomes $2X$ ampere (it increases to twice the value).

(c) Resistivity of a material is the resistance offered by a conductor of that material having unit length and unit area of cross-section: $\rho = \dfrac{RA}{L}$. Its SI unit is ohm-metre ($\Omega\,\text{m}$). The resistivity of an alloy is generally higher than that of its constituent pure metals, and alloys do not oxidise (burn) readily even at high temperatures.

OR

(c)(i) Tungsten is used for lamp filaments because it has a very high melting point (about $3380^\circ\text{C}$) and high resistivity, so it can be raised to a very high temperature and glow white-hot without melting.

(c)(ii) The heating elements of toasters are made of an alloy (e.g. nichrome) rather than a pure metal because an alloy has higher resistivity (produces more heat) and does not oxidise (burn) readily at the high temperatures reached during use, giving it a longer life.