Question

the resistivity of manganese wire of length 1 m is 1.84 × 10 ^-6 home m at 20°c if the diameter of the wire is 3×10 ^-4 m , what will be the resistance of the wire at that temperature

Answer 1

Given :

• Length = 1 m
• Resistivity $\tt \rho = 1.84 \times 10^{-6}$ Ωm .
• Diameter (D) = 3 × $\tt 10^{-4}$
• Temperature (T) = 20 °C

To find :

• The resistance of the manganese wire

Solution :

• The radius of the area of cross section is D/2

$\tt = \dfrac{3}{2} \times 10^{ - 4}$

• Area of the cross section of wire = πr²

$= \tt \dfrac{22}{7} \times \dfrac{3}{2} \times \dfrac{3}{2} \times {10 }^{ - 4} \times {10}^{ - 4}$

$= \tt \dfrac{198}{28} \times {10}^{ - 8} \\ \\ \tt = 7.07 \times {10}^{ - 8} {m}^{2}$

• The resistance of the wire is given by the formula :

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

$\tt = 1.84 \times {10}^{ - 6} \times \dfrac{1}{7.07 \times {10}^{ - 8} }$

$\tt = \dfrac{1.84 \times {10}^{ - 6} \times {10}^{8} }{7.07}$

$\tt = \dfrac{184 \times {10}^{2} }{707}$

$\tt = 26.025 \: \Omega$

Hence the resistance of Manganese wire is 26.025 Ω .

_____________________________

$\underline{ \underline{ \large{ \mathfrak \orange{Resistance : }}}}$

• The property of a matter to oppose the flow of electric current in it is called resistance .
• It is defined as the ratio of potential difference to the current flowing in the circuit .

Resistance vary

1. directly with length .
2. indirectly with area of cross section.
3. Nature of the material.

Answer 2

Answer:

Resistance is 26 ohm

Explanation:

R (resistance) is directly proportional to length (l) and inversely proportional to area of cross-section (A) and p (rho) is constant.

R = p l/A

R = pl/πr²

Given p = 1.84 × 10^-6 ohm m, l = 1 m, d (diameter) = 3 × 10^-4 m and T = 20°C

Area of cross-section = πr²

= 22/7 × 3/2 × 3/2 × 10^-8

= 7.07 × 10^-8 m²

Therefore,

R = 1.84 × 10^-6 × 1/(7.07 × 10^-8)

R = 1.84/7.07 × 10^2

R = 0.26 × 10^2

R = 26 ohm

Hence, the resistance of the wire is 26 ohm.