Question

Q. ​ 100 mg mass of nichrome metal is drawn into a wire of area of cross-section 0.05 mm3. Calculate the resistance of this wire. Given density of nichrome 8.4 x 103 kg/m3 and resistivity of the material as 1.2 x 10-6 Ωm.

Answer 1

Dear student,

● Answer -
R = 5.712 Ω

● Explanation -
# Given -
m = 100 mg = 10^-4 kg
A = 0.05 mm^2 = 5×10^-8 m^2
d = 8.4×10^3 kg/m^3
ρ = 1.2×10^-6 Ωm

# Solution -
Volume of the wire -
V = m / d
V = 10^-4 / 8.4×10^3
V = 1.19×10^-8 m^3

Length of wire is calculated by -
l = V / A
l = 1.19×10^-8 / 5×10^-8
l = 0.238 m

Resistance of nichrome wire -
R = ρl / A
R = 1.2×10^-6 × 0.238 / 5×10^-8
R = 5.712 Ω

Therefore, resistance of wire is 5.712 Ω.

Hope this helped you..