Question

conductor having diameter 0.4 mm has resistivity 5×10 /7 ohm m and its resistance is 40 ohm.What is length of conductor?​

Answer 1

Given

Resistivity (ρ) = 5 × 10-7 Ω m

Resistance (R) = 40 Ω

Diameter (d) = 0.4 mm

d = 4 × 10⁻⁴ m

Hence, we will get  the radius

Radius (r) = 0.0004 mm

r = 0.4 × 10⁻³ m

r = 4.0 × 10⁻⁴ m

We need to find the area of cross-section

A = π$r^{2}$

A = (3.14)(4.0 × 10⁻⁴)2      

A = (3.14)(1.60×10$^{-7}$)  

A = 5.024 × $10^{-7}$ $m^{2}$

Find out

We have to find the length of the wire

Let the length of the wire be L

Formula

As We know that

R = ρ (L) / (A)

L = (R × A) / ρ

Substituting the values in the above equation we get

L = (40 × 5.024 × 10⁻⁷) /  5 × 10-7  m

L = 20.096×10-6 / 5 × 10-7    

L = 40.192 m  

the length of the conductor is 40.192 m

Answer 2

what is conical pendulum show that its time period is given by t=2π