Question

Electrical resistivity of nichrome is 100*10to the power -6ohm metre . calculate the resistance of nichrome wire 110cm long and 0.5 mm diameter?​

Answer 1

Given:-

→ Electrical resistivity of

nichrome = 100×10⁻⁶ Ωm

→ Length of the wire = 110cm

→ Diameter of the wire = 0.5mm

To find:-

→ Resistance of the nichrome wire.

Solution:-

Firstly, let's convert the units of the length and diameter of the wire :-

Length:-

=> 1cm = 0.01m

=> 110cm = 110(0.01)

=> 1.1m

Diameter:-

=> 1mm = 0.001m

=> 0.5mm = 0.5(0.001)

=> 0.0005m

______________________________

Radius of the wire :-

= d/2

= 0.0005/2

= 0.00025m

= 2.5×10⁻⁴ m

Area of the cross section of the wire :-

= πr²

= 3.14×(2.5×10⁻⁴)²

= 19.625×10⁻⁸ m²

______________________________

Now, we know that :-

R = ρL/A

Where :-

• R is the resistance of the wire.

• ρ is the electrical resistivity.

• L is length of the wire.

• A is the cross-sectional area of the wire.

Substituting values, we get :-

=> R = [100×10⁻⁶×1.1]/[19.625×10⁻⁸]

=> R = 110/19.625 × 10⁻⁶⁺⁸

=> R = 5.605×10²

=> R = 560.5 Ω

Thus, resistance of the nichrome wire is 560.5 Ω