Question

The radius of 22-gauge Nichrome wire is 0.32 mm with resistivity rho = 1x10-6 Ω-m. (A) Calculate the resistance for 6 m length of this wire. (B) If a potential difference of 12 V is maintained across the Nichrome wire, what is the current in the wire?

Answer 1

Answer:

(A) Resistance of wire is 18.65 Ω.

(B) Current in the wire is 0.64 A.

Explanation:

Given :

Radius of wire, r = 0.32 mm = 0.32 x 10⁻³ m

Resistivity of wire, ρ = 1 x 10⁻⁶ Ω-m

(A) Length of wire, l = 6 m

Area of the wire, A = πr²

Resistance of the wire, R = (ρl)/A = (ρl)/(πr²)

Substitute the suitable values in the above equation.

$R = \frac{1\times10^{-6}\times6 }{\pi\times(0.32\times10^{-3} )^{2} }$

R = 18.65 Ω

(B) Potential difference, V = 12 volts

Using Ohm's law, V = i x R

Here i is current.

$i=\frac{V}{R}$

Substitute the values in the above equation.

$i=\frac{12}{18.65}$

i = 0.64 A