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 drawn by the thin 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). Ohm's Law is written as:
P = I^2 * R
In this case, we are given the resistance of the wire as 20,000 Ohms and the voltage of the battery as 2.0 Volts. To calculate the current, we can use the formula I = V/R:
I = 2.0 V / 20,000 Ω
I = 0.0001 A (or 100 μA)
Now, we can substitute the calculated current back into the power formula:
P = (0.0001 A)^2 * 20,000 Ω
P = 0.0002 W (or 0.2 mW)
Therefore, the thin copper wire draws a power of 0.2 milliwatts.
Now, let's determine the time it takes for an electron to travel from one end of the wire to the other when the battery is connected.
To do this, we need to know the speed at which electrons move in a conductor. The drift velocity of electrons in copper is typically on the order of millimeters per second. However, for simplicity, let's assume a drift velocity of 1 millimeter per second.
Given the length of the wire is not provided, we cannot provide an exact time. However, if we assume the wire is 1 meter long, and the electron travels at 1 millimeter per second, we can determine the approximate time using the formula:
Time = Distance / Speed
Time = 1 meter / 0.001 meter per second
Time = 1000 seconds
Therefore, if the wire is 1 meter long and the electron travels at a constant velocity of 1 millimeter per second, it would take approximately 1000 seconds for the electron to travel from one end of the wire to the other.