Physics, asked by Pritipandiri2987, 11 months ago

The resistance of a wire of length 2 m and area of cross section 0.5 μm2 is 2.2 Ω. Find the specific resistance of the material of the wire.

Answers

Answered by Cynefin
11

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Answer

♦️GiveN

  • Length of wire = 2m
  • Area of cross section = 0.5μm2
  • Resistance = 2.2 Ohms

♦️To FinD

  • Specific resistance of wire....?

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We must know

➯Specific resistance is the resistance offered for a unit length and per unit area at a particular voltage applied.

Derivation of Formula

➯We know,

\large{ \sf{R \propto \: length \: of \: conductor}} \\ \\  \large{\sf{ \rightarrow \: R  \propto \: l}}.............(1) \\ \\  \large{ \sf{R \propto \:  \frac{1}{area \: of \: cross - section} }} \\  \\  \large{ \sf{ \rightarrow \: R \propto \:  \frac{1}{A} }}.............(2)

From equation (1) and equation (2)

\large{ \sf{  \rightarrow \: R \propto \:  \frac{l}{A} }} \\  \\  \large{ \sf{ \rightarrow \: R =  \boxed{ \rho} \frac{l}{A} }}

Where, is the specific resistivity of the conductor.

➯From the above formula, we can write

 \large{ \rightarrow  \boxed{ \purple{ \sf{\rho =  \frac{RA}{l} }}}}

♦️Note:

Symbols have their usual meanings

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♦️As we can see, All the unitsof physical quantities are not according to a particular metric system, Lets convert it into their respective SI units.

Unit Conversion

➯Resistance = 2.2 ohms

Ohms, is the SI unit only, No change is needed.

➯Length = 2m

Metre is the SI unit only, No change is needed.

➯Area = 0.5μm^2

μm^2 is not the SI unit unit , instead m^2 is the SI unit, So we need to convert it

\large{ \sf{\rightarrow \: 1   micro-m =  {10}^{ - 6} m}} \\  \\ \large{ \sf{\rightarrow \: 1 \:micro- {m}^{2}  =  {10}^{ - 12}  {m}^{2} }} \\ \\

Then, 0.5 μm^2 =

\large{ \sf{\rightarrow \: 0.5 \:micro- {m}^{2} =  0.5 \times  {10}^{ - 12}  {m}^{2} }} \\  \\  \large{ \:  \boxed{ \sf{ = 5 \times  {10}^{ - 13}  {m}^{2} }}}

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✰Solution✰

➯By using formula,

\large{\sf{\rightarrow \rho \:  =  \frac{RA}{l}}}

Putting the values of R, A and l

 \large{ \sf{ \rightarrow \rho \:  =  \frac{  1.1\:  \: \cancel{2.2}\times 5 \times  {10}^{ - 13} }{ \cancel{2}}   \: ohm  - m}} \\  \\  \large{\sf{ \rightarrow \:  \rho \:  =  1.1 \times 5 \times  {10}^{ - 13} \: ohm - m}} \\  \\  \large{ \rightarrow \:  \boxed{ \purple{ \sf{ \rho = 5.5 \times  {10}^{ - 13}  ohm - m}}}}

 \large{ \boxed{ \sf{ \dag{ \green{ \: specific \: resistivity \: of \: the \: wire = 5.5 \times  {10}^{ - 13} ohm - m}}}}}

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Answered by akshat29605
0

Answer:

THE ANS IS 5.5*10-13 OHM

Explanation:

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