Animated Solution for Physics - Current Electricity: Consider four conducting materials copper, tungsten, mercury and aluminium with resistivity ${\rho }_C,{\rho }_T,{\rho }_M$ and ${\rho }_A$, respectively. Then,

When we talk about how well a material conducts electricity, we often use the term 'resistance'. However, resistance depends on the shape and size of the object. To truly compare the fundamental conducting nature of different materials, we use resistivity ($\rho$). Resistivity is an intrinsic property that quantifies how strongly a given material opposes the flow of electric current, independent of its dimensions.

In this problem, we are asked to compare the resistivities of four distinct materials: Copper (${\rho }_C$), Aluminium (${\rho }_A$), Tungsten (${\rho }_T$), and Mercury (${\rho }_M$). Let's embark on a journey through their atomic structures to understand their electrical behavior.

The Champions of Conduction

Let's start with the materials that power our modern world. Copper is renowned for being an exceptional conductor. Its atomic structure allows its outermost electrons to roam freely with minimal scattering, resulting in a very low resistivity of approximately $1.68\times 10^{-8}\Omega \cdot m$. This is why Copper is the undisputed king of household electrical wiring.

Aluminium, on the other hand, is also a fantastic conductor, but it is slightly more resistive than Copper, clocking in at about $2.65\times 10^{-8}\Omega \cdot m$. You might wonder, if Copper is better, why do we use Aluminium for massive overhead transmission lines? The secret lies in its density. Aluminium is much lighter than Copper. A thicker Aluminium wire can carry the same current as a thinner Copper wire while still weighing significantly less, which drastically reduces the structural strain on transmission towers.

From this, we can establish our first inequality: ${\rho }_C<{\rho }_A$.

The Glowing Resistor

Next, we have Tungsten. Think about where you encounter Tungsten in daily life. It is the classic material used for the filaments in traditional incandescent light bulbs. The goal of a filament is not just to let current pass through easily; it needs to resist the current enough to generate intense heat ($P=I^{2}R$) so that it glows white-hot.

To achieve this without melting, Tungsten possesses the highest melting point of all pure metals (around $3422^{\circ }\text{C}$) and a notably higher resistivity than our wiring metals, approximately $5.60\times 10^{-8}\Omega \cdot m$.

This gives us our next piece of the puzzle: ${\rho }_A<{\rho }_T$.

The Liquid Outlier

Finally, we arrive at Mercury. Mercury is unique among these four because it is a liquid at room temperature. In solid metals like Copper or Tungsten, the atoms are arranged in a highly ordered, periodic crystal lattice. According to quantum mechanics, electron waves can travel through a perfectly periodic lattice without any scattering. Resistance only arises due to imperfections and thermal vibrations (phonons).

However, in a liquid like Mercury, this beautiful periodic order is completely shattered. The atoms are in a disordered, chaotic state. When free electrons try to navigate through this chaotic sea of atoms, they experience massive and frequent scattering. This drastically reduces their mean free path, causing the resistivity to skyrocket. Mercury's resistivity is roughly $98\times 10^{-8}\Omega \cdot m$, making it by far the most resistive material on our list.

This solidifies our final inequality: ${\rho }_T<{\rho }_M$.

By chaining our logical deductions together, we get the complete order of resistivities from lowest to highest:

Reversing this to match the format of the options, we find that Mercury is the most resistive, followed by Tungsten, then Aluminium, and finally Copper:

Looking closely at the given options, option (d) states ${\rho }_M>{\rho }_A>{\rho }_C$, which perfectly aligns with our derived physical reality.