Question

The resistivity of copper is 1.7 × 10-8 Ωm. What length of copper wire of diameter 0.1 mm will have a resistance of 34Ω?

Answer 1

Answer:

To find lenth of copper, when

Resistance(R) =34 ohm

Diameter = 0.1mm =0.1 /(10x10x10)m

Resistivity (p) =1.7/(10x10x10x10x10x10x10x10) m

Explanation:

Let, lenth be'L'

Area of cross-section (A) = 0.1×3.14×0.1/(10x10x10×4) =0.00000785 m

R =(p×L) /A

So, (34×A) /p = L

Hence, L= 15,700 m

Answer 2

Length of the wire = 15.7 m

Explanation:

Given:  

Resistance (R) =34 Ω

Diameter of wire = 0.1 mm = 0.1 * 10^-³ m

Resistivity of copper (p) = 1.7 * 10^-8  Ωm

Find: Length of wire L

Solution:

Cross-section area of the copper wire = πr²  = 3.14 * 0.1 * 0.1 * 10^-6  / 4

= 3.14 * 0.1 * 0.1 * 10^-6 / 4

/(10x10x10×4) =0.00000785 m

We know that R = pL / A

So L = (34 * A) /p  

= (34 * 3.14 * 0.1 * 0.1 * 10^-6 / 4) / 1.7 * 10^-8  

= 5 * 3.14

Therefore L = 15.7 m