Question

Calculate the area of cross- section of a wire, if its length is 1.0m, its resistance is 32 Ω and resistivity of the material is 1.6 ×10-8 Ω m.​

Answer 1

Given :

Length of wire = 1 m

Resistance = 32Ω

Resistivity = 1.6 × 10‾⁸ Ω m

To Find :

Area of cross section of the wire.

Solution :

❖ We know that resistance of a conductor is directly proportional to the length of conductor and inversely proportional to the area of cross section.

Mathematically, $\bf{R\propto\dfrac{L}{A}}$

Putting proportionality constant, we get

$\bigstar\:\underline{\boxed{\bf{\orange{R=\rho\times\dfrac{L}{A}}}}}$

Where ρ denotes resistivity of conductor

By substituting the given values;

$\sf:\implies\:R=\rho\times\dfrac{L}{A}$

$\sf:\implies\:32=1.6\times10^{-8}\cdot\dfrac{1}{A}$

$\sf:\implies\:A=\dfrac{16\times10^{-9}}{32}$

$\sf:\implies\:A=0.5\times10^{-9}$

$:\implies\:\underline{\boxed{\bf{\purple{A=5\times10^{-10}\:m^2}}}}$

Answer 2

Given

length= 1.0m

resistance = 32Ω

resistivity= 1.6× 10^-8 Ωm

To find

Calculate the area of cross- section of a wire.

Solution

♦️ Factors on which Resistance Depends

Material- the resistance is different for different wires of same length and thickness

area of cross- section- the resistance is greater for thick wire

$\boxed { \blue{R \: \alpha \: \frac{1}{A} }}$

length- the resistance is directly proportional to the length.

$\boxed { \blue{R \: \alpha \: l }}$

temperature- resistance increases with the increase in temperature.

$\boxed { \blue{R \: \alpha \: \frac{l}{A} }}$

putting proportionality constant, we get

$\underline{\boxed{\bf{\blue{R=\rho\times\dfrac{L}{A}}}}}$

• where rho is the called resistivity of the material.

Now substitute values in the above formula:-

$\bold{\to \: 32 = 1.6 × {10}^{ - 8} × \frac{1}{A} }\\ \\ </p><p> \bold{ \to \: A = \frac{16 × {10}^{ - 9} }{32}} \\ \\ </p><p> \bold{ \to \: A = 0.5 × {10}^{ - 9}} \\ \\ </p><p> \to \bold \blue{\: A= 5 × {10}^{ - 10} \: m² }$

So the area of cross- section is 5 × 10 ^-10 m².

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Power Booster !!

❄️ metals have low resistivity.

❄️ insulators have high resistivity.

❄️ alloys have larger resistivity and metals.

( suitable for heating elements of iron, toasters e.g nichrome. Their resistance does not vary with temperature)

❄️ semiconductors resistivity lies between conductors and insulators.

❄️superconductors are substances which offer no resistance at critical temperature such that current passes through it without any loss of energy..

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