Question

A 10Ω resistor is made from a wire of length 100m and resistivity 4 × 10^-9Ωm. Taking π = 22/7. The length of the wire required is​___________.

a) 50 m
b) 100 m
c) 200 m
d) 400 m

Answer 1

The length of the wire required to make a 10Ω resistor is approximately 4914 m.

Step-by-step explanation:

To calculate the length of the wire required to make a 10Ω resistor, we can use the formula:

R = (ρ * L) / A

Where R is the resistance, ρ is the resistivity, L is the length, and A is the cross-sectional area of the wire. Rearranging the formula, we have:

L = (R * A) / ρ

The cross-sectional area of the wire can be calculated using the formula:

A = (π * r^2)

Substituting the given values into the equations, we have:

A = (22/7 * (0.25/100)^2) = 0.0019634954 m^2

L = (10 * 0.0019634954) / (4 x 10^-9) = 4913.73835 m ≈ 4914 m

Therefore, the length of the wire required to make a 10Ω resistor is approximately 4914 m.