Question

A potential difference of 1.40 V will be applied to a 41.00 m length of 18-gauge tungsten wire (diameter = 0.0400 in). Calculate the current.

Calculate the magnitude of the current density.

Calculate the magnitude of the electric field within the wire.

Calculate the rate at which thermal energy will appear in the wire.

Answer 1

Write the equation for current, i=- R 4 PL You know that R=- 102 Thus, Adv 4pl Substitute the value 0.04 in for d, 1.4V for V, 1.69x10* 2.m for p and 41 m for L. . 3.14 x(0.04 inx 0.0254 m/inºx(1.4) i= 4x(1.69x10-82m)(41 m) = 1.64 A The current in the wire will be 1.64A. b) Write the equation for the magnitude of current density, A Substitute the value 1.64 A for i and 1.016x 10m ford.

J =- 4x(1.64 A) 3.14x(1.016x10 m) = 2.02x10Alm? Hence, the magnitude of current density is 2.02x100 A/m²). The electric field in the wire, E = Substitute 1.4 V for V and 41 m for L. E = 1.4V 41 m = 3.41x10-2V/m Thus, the electric field within the wire will be|3.14x10-2 V/m . d) The rate at which thermal energy appears will be given by the equation of power. P=Vi Substitute the value 1.4V for V and 1.64 A for i. P = (1.4V)(1.64A) = 2.296 W Therefore, the rate at which themmal energy will appear in the wire is 2.296 W.