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What is meant by electrical resistivity of a material? Derive its S.I. unit. Describe an experiment to study the factor on which the resistance of a conducting wire depends.
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Answer 1

Correct Question-:

• What is meant by electrical resistivity of a material ? Derive its S.I. unit. Describe an experiment to study the factor on which the resistance of a conducting wire depends.

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AnswEr-:

• $\frak{1^{st} \: Part \:of\:Question -:} \begin{cases} \sf{What\: is \:meant\: by\: electrical\: resistivity\: of \:a\: material\:? }\end{cases}$

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Solution of 1st Part -:

• Electrical Resistivity of a Material -: Electrical Resistivity of the material of the conductor is the Electrical Resistance offered by the conductor of per unit length with per unit of cross sectional area at a specified temperature.

• Numerical Form of Electrical Resistivity-:

• $\boxed {\implies{\sf{\large { \rho = R \: \frac{A}{L}}}}}$

• $\frak{Here \:\: -:} \begin{cases} \sf{ \rho \:= \frak{Electrical\:Resistivity}} & \\\\ \sf{R \:=\:\frak{Resistance}\: ,} & \\\\ \sf{\: A =\frak{Area}}& \\\\ \sf{ L = \frak{ Length}}\end{cases}$

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• $\frak{2^{nd} \: Part \:of\:Question -:} \begin{cases} \sf{Derive \: S.I \: Unit \; of \: Electrical \:Resistivity \:of\:Material. }\end{cases}$

Solution of 2nd Part -:

As ,We know that ,

• $\implies{\sf{\large {\rho = R \frac{A}{L}}}}$

• $\frak{Here \:\: -:} \begin{cases} \sf{ \rho \:= \frak{Electrical\:Resistivity}} & \\\\ \sf{Resistance \:=\:\frak{R}\: = ohm \: or\: \Omega ,} & \\\\ \sf{\: A =\frak{Area}= metre^{2}}& \\\\ \sf{ L = \frak{ Length}= metre}\end{cases}$

• $\implies{\sf{\large { \rho = \frac{R \times A}{L}}}}$

• $\implies{\sf{\large { \rho = \frac{Ohm\:or\: \Omega\:×metre^{2}}{metre}}}}$

• $\implies{\sf{\large { \rho = \Omega \:or\:ohm\; \times Metre}}}$

Hence ,

• The S.I Unit of Electrical Resistivity of material is -:
• $\underline{\boxed{\star{\sf{\blue{  ohm \times metre \: or \:( \Omega \times metre)}}}}}$

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• $\frak{3^{rd} \: Part \:of\:Question -:} \begin{cases} \sf{ Describe \:an \:experiment \:to\: study\: the\: factor}& \\\\ \sf{\: on\: which \:the \:resistance\: of \:a \:conducting \:wire \:depends\:. }\end{cases}$

Solution of 3rd Part -:

$\boxed{\huge{\bf{\sf{Required \:Experiment \:-:}}}}$

Aim -:

• To study the factor on which the resistance of a conducting wire depends.

• $\frak{Materials \: Required -:} \begin{cases} \sf{ A \:Cell}& \\\\ \sf{\: A\: Nichrome \:wire . \: }& \\\\ \sf{\: An\: ammeter \: . \: }& \\\\ \sf{\: A\: Copper \:wire . \: }\end{cases}$

To Do -:

• 1st Step -:
• Complete an Electrical Circuit consisting of a cell an ammeter , a nichrome wire of length L( marked 1 in attachment) and plug a key .
• Note the Current in the ammeter

• 2nd Step -:
• Now , Replace the nichrome wire by another nichrome wire of same thickness but twice the length that is 2L ( marked 2 in attachment )
• Note the ammeter reading .

• 3rd Step -:
• Replace the wire by the thicker nichrome wire of the same length L and ( marked 3 in attachment ) A thicker wire has a larger cross sectional area.
• Note down the current through the circuit.

• 4th Step -:
• Instead of taking nichrome wire , connect a copper wire ( marked 4 in attachment ) in the circuit . Let the wires of the same length and same area of cross section as that of the first nichrome wire ( marked 1 in attachment).
• Note the value of current .

Observation-:

• It is observed that the ammeter reading decreases to one -half when the length of wire is doubled . The ammeter reading is increased when a thicker wire of the same material and of the same length is used in the circuit . A change in ammetre reading is observed when a wire of different material of the same length and the same cross section is used .

Conclusion-:

• We observed that the resistance of the conductor depends -:
• 1) on its length ,
• 2) on its area of cross section , and
• 3 ) on the nature of the material .

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Answer 2

Electrical Resistivity:

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎The quantification of the ability of a material to oppose the flow of electric current is called as electricity resistivity. It is denoted by a Greek symbol $\rho$. The electrical resistivity varies according to the type of material. Metals have less resistivity as it is a good conductor of electricity. While comparing to this, non-metallic materials have high resistivity. It S.I. unit is "Ohm metre"The electrical resistivity of a material can be calculated by using the formula:

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎${\boxed{\rho=R\:\dfrac{A}{l}}}$

• $\sf{\rho=Resistivity}$
• $R=\sf{Resistance}$
• $A=\sf{Area\:of\:cross\:section}$
• $l=\sf{Length\:of\:the\: wire}$

Derivation of S.I. unit of resistivity:

We know the formula to calculate the resistivity of a material. Now, let's derive its S.I. unit. First, we shall recall the S.I. unit of resistance, area and length.

$\begin{gathered} \begin{array}{|c|c|} \sf Resistance & \Omega \\ \sf Area & \sf {m}^{2} \\ \sf Length & \sf m\end{array}\end{gathered}$

Now, insert the S.I. units in the formula in their respective places.

$\:$

$:\implies{\sf{Resistivity=\Omega\times \dfrac{m^2}{m}}}$

$\:$

Cancel metre from sq.metre-

$\:$

$\:\:\:\::\implies{\sf{\rho=\Omega\times \dfrac{\cancel{m}\:^2}{\cancel{m}}}}$

$\:$

Now we get,

$\:$

$\:\:\:\:\:\:\::\implies{\sf{\rho=\Omega\times m}}$

$\:$

$\:\:\:\:\:\:\:\:\:\:\::\implies\underline{\sf{\red{\rho=\Omega\:metre}}}$

$\:$

Hence, the S.I. unit of Resistivity is "Ohm metre".

‎

‎

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎‎ ${\boxed{\sf{Required\:experiment}}}$

Aim:

‎ ‎ ‎ ‎ ‎To study the factor on which the resistance of a conducting wire depends.

Materials Required:

• A cell
• Nichrome wire
• Copper wire
• An ammeter

Method:

1. First, make a complete electrical circuit with a cell, an ammeter and nichrome wire.
2. Note the reading shown in the ammeter.
3. Now, replace the nichrome wire of same thickness with twice the length of first.
4. Look at the ammeter and note down the reading.
5. Replace the nichrome wire with another nichrome wire of higher thickness and large cross-section area and note the reading shown.
6. Now, replace the nichrome wire with a copper wire having same length and f cross-section area.
7. Note down the current flowed shown in the ammeter.
8. Observe all the noted readings!

Observation:

‎ ‎ ‎ ‎ ‎ ‎ ‎The ammeter reading decreases to half when the length of wire is doubled. When wire with high thickness is used, the reading was increased. When copper wire is used, change in reading can be observed.

Conclusion:

‎ ‎ ‎ ‎ ‎ ‎ ‎Resistance of a wire depends on various factors such as length, area of cross-section and the material's nature.

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