How long would it take for a net charge of 2.5 C to pass a location in a wire if

Question

How long would it take for a net charge of 2.5 C to pass a location in a wire if it is to carry a steady current of 5.0 mA? If the wire is actually connected directly to the two electrodes of a battery and the battery does 25 J of work on the charge during this time, what is the terminal voltage of the battery? What is the resistance of the wire? If the wire has a length of 25 m, and a radius of 10.55 mu m, what is the material from which the wire is made? You must show how you arrive at your choice. What electric field exists within the wire?

Explanation / Answer

5)

A) I= 5.0 mA = 5.0 x 10-3 Columbs/second

I = 5.0x10-3 A

current = charge / time
I = Q / t

Since you want time, rearrange:
t = Q / I = (2.5 C)/(5.0x10-3) = 500 seconds = 8.3 mins

B) E = Q.V where E is the energy in joules, Q the charge in coulombs, and V the voltage in volts
25 = 2.5 x V
V = 10 Volts

C) The resistance of the wire, R= V/I = 10/(5.0x10-3) = 2000 = 2k

D) R= L/A , where is the resistivity

A is cross sectional area of the wire = r2 = 3.14x(10.55x10-6) = 3.5x10-10 m2

Length of the wire, L = 25 m

   = RA/L = (2000x3.5x10-10)/25 = 2.8x10-8 .m

The wire used is Aluminium

E) V= E.L

Electric field, E = V/L = 10/25 = 0.4 V/m

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