Question

At 25°v the resistance of a given wire of length 1m and diameter 0.5mm is 25 . What is the resistivity of the wire at this temperature ?

Answer 1

Explanation:

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12th

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Current Electricity

Electrical Resistance & Resistivity

Resistance of a metal wire ...

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Asked on December 26, 2019 by

Angèliña Kadam

Resistance of a metal wire of length 1 m is 26Ω at 20

∘

C. If the diameter of the wire is 0.3 mm, what will be the resistivity of the metal at that temperature? Using Table 12.2. predict the material of the wire.

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ANSWER

R=26 Ω

l=1m

d−0.3mm

r=

2

d

=

2

0.3×10

−3

=0.15×10

−3

m

A=πr

2

=3.14×(0.15×10

−3

)

2

=0.071×10

−6

m

2

R=

A

ρL

or ρ=

l

RA

=

1

26×0.071×10

−6

=1.84×10

−6

Ωm

Please mark it

Answer 2

Answer: 127.38 ohms-meter.

Given: Length of wire = 1m, diameter = 0.5mm and resistance is 25 ohms at 25°C.

To Find: Resistivity of the wire.

Step-by-step explanation:

Step 1: Resistance:

A conductor's ability to resist the flow of current through it is known as resistance.

The interaction between the applied voltage and the electric current flowing through it controls it.

Step 2: Resistance of a wire:

A wire's resistance is directly correlated with its length and inversely correlated with its cross-sectional area. Additionally, the conductor's material has an impact on resistance.

Ohm's law explains the fundamental behaviour of electrical circuits. Current, resistance, and voltage are all closely connected.

Resistance is a constant that is unaffected by current or voltage, according to Ohm's law.

If the length, cross-sectional area, and resistivity of the material are known, the resistance of a wire can be computed as follows:

$R=\rho\frac{L}{A}$

Where R is the resistance, $\rho$ is the resistivity of the wire, L is the length of the wire and A is the area of the cross-section of the wire.

The length of the wire – Longer the wire, the greater its resistance.

The greater the cross-sectional area, the less resistance it experiences.

The material's resistivity determines how resistant it is; the higher the resistivity, the more resistant it is.

Ohm's Law can be used to compute resistance if the voltage and current in a circuit are known.

$R=\frac{V}{i}$

Step 2:

R = 25 Ω

l = 1 m

d = 0.5 mm

r = 0.25 mm

d = $5\times10^{-4}$m

$A=\pi r^2$

$=3.14\times(0.25\times10^{-3})^2\\\\=0.1961\times10^{-6} m^2$

$R=\rho\frac{L}{A}\\\\\rho=\frac{RA}{L} =\frac{250\times 0.1961\times 10^{-6}}{1}=127.38$

Hence, correct answer is 127.38 ohms-meter.

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