a very thin piece of copper wire has an electrical resistance of 20,000 Ohms. You connect its ends to a regular 2.0 Volt battery. How much power does it draw? Let's assume that this little piece of wire initially contained one trillion (that's a one with 12 zeros) mobile electrons which participate in the electric current flowing through it. How long does it take for an electron that was at one end of the wire when the battery was connected to travel to the other end?

To calculate the power consumed by the copper wire, we can use Ohm's Law, which states that power (P) is equal to the square of the current (I) multiplied by the resistance (R).

P = I² * R

First, we need to calculate the current flowing through the wire using Ohm's Law, which states that current (I) is equal to the voltage (V) divided by the resistance (R).
I = V / R

Given that the resistance (R) of the copper wire is 20,000 Ohms and the voltage (V) of the battery is 2.0 Volts, we can substitute these values into the formula to find the current (I):
I = 2.0 V / 20,000 Ω
I = 0.0001 Amperes (A)

Now that we know the current, we can calculate the power consumed by the wire using the formula mentioned earlier:
P = I² * R
P = (0.0001 A)² * 20,000 Ω
P = 0.00000001 Watts (W)

Therefore, the power consumed by the thin copper wire is 0.00000001 Watts or 10 nanowatts (nW).

Regarding the time it takes for an electron to travel from one end of the wire to the other, we need to consider the drift velocity of the electrons.

The drift velocity refers to the average speed with which electrons move in a conducting material. In the case of copper, the drift velocity is around 0.02 mm/s.

Since the wire is very thin, it is reasonable to assume that all the mobile electrons spread evenly throughout the wire at the beginning. Therefore, the distance the electron must travel to reach the other end of the wire is equal to the length of the wire.

Let's assume the length of the wire is L meters (given that the actual length is not specified in the question). The time it takes for an electron to travel from one end to the other can be calculated using the formula:
Time = Distance / Velocity
Time = L / 0.02 mm/s

However, we are given that the length of the wire initially contained one trillion mobile electrons (1,000,000,000,000). In this case, we need to divide the length of the wire by the number of electrons to determine the distance each electron needs to travel:
Distance per Electron = L / Number of Electrons
Distance per Electron = L / 1,000,000,000,000

Thus, the time it takes for an electron to travel from one end of the wire to the other can be calculated as:
Time = (L / 1,000,000,000,000) / 0.02 mm/s

Please provide the length of the wire (in meters) for a precise calculation of the time it takes for an electron to travel from one end to the other.