Which of the following has the highest value of resistivity?
Nichrome
Understanding Electrical Resistivity of Materials
Electrical resistivity ($\rho$) is a fundamental property of a material that measures how strongly it resists the flow of electric current. A low resistivity indicates a material that allows electric current to flow easily, making it a good conductor. Conversely, a high resistivity indicates a material that resists current flow, making it a poor conductor or an insulator. Resistivity is measured in ohm-meters ($\Omega \cdot \text{m}$).
The question asks us to identify which among the given materials has the highest value of resistivity. Let's consider the typical resistivity values for each material:
- Silver: Silver is known to be one of the best electrical conductors, meaning it has very low resistivity. Its resistivity is approximately $1.59 \times 10^{-8} \ \Omega \cdot \text{m}$ at $20^\circ\text{C}$.
- Chromium: Chromium is a metal. Its resistivity is higher than that of silver, typically around $1.25 \times 10^{-7} \ \Omega \cdot \text{m}$ at $20^\circ\text{C}$.
- Iron: Iron is also a metal. Its resistivity is higher than silver and close to that of chromium, approximately $9.71 \times 10^{-8} \ \Omega \cdot \text{m}$ at $20^\circ\text{C}$.
- Nichrome: Nichrome is an alloy, primarily composed of nickel and chromium. Alloys are often designed to have specific properties, and nichrome is well-known for its high resistivity and resistance to oxidation at high temperatures. It is commonly used in heating elements. The resistivity of nichrome is significantly higher than that of typical metals, approximately $1.10 \times 10^{-6} \ \Omega \cdot \text{m}$ at $20^\circ\text{C}$.
Let's compare these values directly:
| Material | Approximate Resistivity ($\Omega \cdot \text{m}$ at $20^\circ\text{C}$) |
|---|---|
| Silver | $1.59 \times 10^{-8}$ |
| Chromium | $1.25 \times 10^{-7}$ |
| Iron | $9.71 \times 10^{-8}$ |
| Nichrome | $1.10 \times 10^{-6}$ |
Looking at the table, we can see that the resistivity values are:
- Silver: $0.0159 \times 10^{-6} \ \Omega \cdot \text{m}$
- Chromium: $0.125 \times 10^{-6} \ \Omega \cdot \text{m}$
- Iron: $0.0971 \times 10^{-6} \ \Omega \cdot \text{m}$
- Nichrome: $1.10 \times 10^{-6} \ \Omega \cdot \text{m}$
Comparing these values, $1.10 \times 10^{-6} \ \Omega \cdot \text{m}$ (Nichrome) is the largest value.
Therefore, Nichrome has the highest value of resistivity among the given options.
Revision Table: Comparing Resistivity Values
Understanding the typical resistivity values of common materials helps in comparing their electrical properties.
| Material Type | Material | Resistivity ($\Omega \cdot \text{m}$) | Conductivity ($\text{S/m}$) |
|---|---|---|---|
| Good Conductor (Metal) | Silver | $1.59 \times 10^{-8}$ | $6.30 \times 10^{7}$ |
| Good Conductor (Metal) | Copper | $1.68 \times 10^{-8}$ | $5.96 \times 10^{7}$ |
| Good Conductor (Metal) | Aluminium | $2.82 \times 10^{-8}$ | $3.50 \times 10^{7}$ |
| Metal | Iron | $9.71 \times 10^{-8}$ | $1.03 \times 10^{7}$ |
| Metal | Chromium | $1.25 \times 10^{-7}$ | $8.00 \times 10^{6}$ |
| Alloy (Resistive) | Nichrome | $1.10 \times 10^{-6}$ | $9.09 \times 10^{5}$ |
| Semiconductor | Silicon | $6.40 \times 10^{2}$ (pure) | $1.56 \times 10^{-3}$ (pure) |
| Insulator | Glass | $10^{10}$ to $10^{14}$ | $10^{-14}$ to $10^{-10}$ |
Additional Information on Resistivity and Conductivity
Resistivity ($\rho$) and electrical conductivity ($\sigma$) are inversely related properties of a material. Conductivity measures how well a material conducts electric current, while resistivity measures how well it resists it. The relationship is given by $\sigma = 1/\rho$. Good conductors have low resistivity and high conductivity. Poor conductors (or insulators) have high resistivity and low conductivity.
Materials are generally classified based on their resistivity:
- Conductors: These materials have very low resistivity, typically in the range of $10^{-8} \ \Omega \cdot \text{m}$. Metals like silver, copper, and gold are excellent conductors.
- Semiconductors: These materials have resistivity values between conductors and insulators, typically in the range of $10^{-5}$ to $10^{3} \ \Omega \cdot \text{m}$. Silicon and germanium are common examples. Their conductivity can be significantly changed by adding impurities (doping).
- Insulators: These materials have very high resistivity, typically in the range of $10^{10}$ to $10^{16} \ \Omega \cdot \text{m}$. Materials like rubber, glass, wood, and plastics are good insulators.
Alloys, like Nichrome, are often specifically formulated to achieve desired resistivity values that are different from their constituent pure metals. Nichrome's high resistivity makes it ideal for applications where heat generation due to current flow is needed, such as in toasters, hair dryers, and other electric heaters.
Important Questions from Resistivity of Various Materials
What is the correct sequence of resistivity of silver, nichrome and glass at room temperature?
Which of the following graph correctly represents the variation of resistivity 's' with temperature 'T' for a semiconductor material ?
The correct sequence of increasing order of electrical resistivity of the given material is-
- Resistivity of a conductor depends on
