What is the resistance of an aluminum wire of length l = 10.9 m and diameter = 1

Question

What is the resistance of an aluminum wire of length l = 10.9 m and diameter = 1.30 mm? The resistivity of aluminum is 2.82 middot10^-8 Ohm m. Three capacitors with capacitances C1 = 3.50 nF, C2 = 2.30 nF, and C3 = 4.80 nF are wired to a battery with V = 16.0 V, as shown in the figure. What is the potential drop across capacitor C2? What is the current density in an aluminum wire having a radius of 2.00 mm and carrying a current of 1.00 mA? What is the drift speed of the electrons carrying this current? The density of aluminum is 2.70 middot 10^3 kg/m^3, and 1 mole of copper has a mass of 26.98 gram. There is one conduction electron per atom in Aluminum.

Explanation / Answer

1)

for the resistance

Resistance = p * L/A

Resistance = 2.82 *10^-8 * 10.9/(pi * (0.0013/2)^2)

Resistance = 0.232 Ohm

the resistance is 0.232 Ohm

2)

for the net capacitor

1/Cnet = 1/(C2 + C3) + 1/C1

1/Cnet = 1/(4.80 + 2.30) + 1/3.50

Cnet = 2.344 nF

Now , for the potential drop across C2

voltage across C2 = 2.344 * 16/(4.80 + 2.30)

voltage across C2 = 5.282 V

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