Question

A 580-mm long tungsten wire, with a 0.046-mm-diameter circular cross section, is wrapped around in the shape of a coil and used as a filament in an incandescent light bulb. When the light bulb is connected to a battery, a current of 0.526 A is measured through the filament.
Required:
a. How many electrons pass through this filament in 5 seconds?
b. How many electrons pass through this filament in 5 seconds?
c. What is the resistance of this filament? What is the resistance of this filament?
d. What is the voltage of the battery that would produce this current in the filament?

Answer 1

Answer:

a,b)   #_ {electron} = 1.64 10¹⁹ electrons, c)  R = 19.54  Ω, d)   V = 10.3 V

Explanation:

a and b) The current is defined as the number of electrons that pass per unit of time

let's look for the load

            Q = I t

            Q = 0.526  5

            Q = 2.63 C

Let's use a direct rule of three proportions. If an electron has a charge of 1.6 10⁻¹⁹ C, how many electrons does 2.63 C have?

           #_ {electron} = 2.63 C (1 electron / 1.6 10⁻¹⁹)

           #_ {electron} = 1.64 10¹⁹ electrons

         

c) the resistance of a wire is given by

          R = ρ l / A

           

where the resistivity of tungsten is 5.6 10⁻⁸ Ω

the area of ​​the wire is

           A = π r2 = π d²/4

         

we substitute

            R = $\rho \ l \ \frac{4}{\pi d^2}$

let's calculate

           R = 5.6 10⁻⁸  0.580 $\frac{4}{ \pi (0.046 \ 10^{-3})^2 }$

           R = 19.54  Ω

d) let's use ohm's law

           V = i R

            V = 0.526 19.54

            V = 10.3 V