Question

The power through a cylindrical resistor is 1.5 W. If the radius of this resistor is 5.2 mm and its length is 2.8 cm, calculate the magnitude of the current density. The resistivity of this resistor is 3.8 x10^-5 Ω. m.

Select one:

a. 1.3x10⁵ A/m²

b. 3.3x10⁵ A/m²

c. 4.3x10⁵ A/m²

d. 2.3x10⁵ A/m²

Answer 1

Area of the resistor, A = * R²
Where R is the radius of the resistor.
A = * (5.2 * 10^-3)²
= 84.95 * 10^-6 m²
Length of the resistor, L = 2.8 cm = 0.028 m
Resistivity of the resistor, = 3.8 * 10^-5m
----------------------------------------------------------
Resistance, R = ( * L) / A
= [(3.8 * 10^-5) * 0.028] / (84.95 * 10^-6)
= 0.0125
---------------------------------------------------------
Power through the resistor, P = I² * R
I² = P/R
I = SQRT[P/R]
= SQRT[1.5 / 0.0125]
= SQRT[119.76]
= 10.94 A
----------------------------------------------------------
Current density, J = I/A
= 10.94 / (84.95 * 10^-6)
= 1.3 * 10⁵ A/m²(option a)